The Economics of Financial Markets

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Author: Hendrik S. Houthakker | Peter J. Williamson

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THE ECONOMICS OF FINANCIAL MARKETS

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Hendrik S. Houthakker and Peter J. Williamson

New York Oxford OXFORD UNIVERSITY PRESS 1996

Oxford University Press Oxford New York Athens Auckland Bangkok Bogota Bombay Buenos Aires Calcutta Cape Town Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madras Madrid Melbourne Mexico City Nairobi Paris Singapore Taipei Tokyo Toronto and associated companies in Berlin Ibadan

Copyright © 1996 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 198 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Houthakker, Hendrik S. The economics of financial markets / Hendrick S. Houthakker and Peter J. Williamson. p. cm. Includes bibliographical references. ISBN 0-19-504407-X 1. Capital market. 2. Capital market—United States. 3. Stock —exchange. 4. Futures market. I. Williamson, Peter I. II. Title. HG4523.H68 1995 332.63'2'0973—dc20 94-3949

5 7 9 8 6 4

Printed in the United States of America on acid-free paper

Preface

Does economics have anything useful to say about the financial markets? The fact that most large financial firms employ sizable staffs of economists indicates that it does. During the last three decades the study of these markets has been transformed by a number of eminent scholars, several of whom subsequently received the Nobel prize in economics. The most illuminating of their contributions were the statement of the Efficient Market Hypothesis in its various forms, of the Capital Assets Pricing Model, and of options pricing theory. These subjects are taken up in Chapters 5, 6, and 8, respectively. In addition, Chapter 2 draws in part on Irving Fisher's theory of interest rates, Chapter 4 on Markowitz's analysis of portfolio selection, and Chapter 7 on Tobin's comparison of asset values and Porter's ideas on business strategy, while Chapter 10 owes much to Working's insights into futures trading. This academic work has had a significant impact on the actual operation of financial markets. Although we have tried to do justice to these various ideas, we have not treated them as dogmas. By referring to empirical evidence as much as possible, we have sought to give readers a critical understanding of their validity. In the same spirit we have devoted considerable attention to certain institutional details. Thus we have stressed the importance of transaction costs, which are often assumed to be zero in theoretical analyses. Without explicit consideration of transaction costs it is difficult, for example, to understand the standardization that is characteristic of successful financial markets. Some knowledge of institutional details is also necessary for an intelligent perusal of the financial press. Another feature of this book is the frequent presentation of statistical data in tables or graphs. These serve not only to give readers a sense of proportion but also to acquaint them with possible sources for any research they may wish to

VI

PREFACE

undertake themselves. We believe that some of these statistics cannot be easily found elsewhere. For the sake of truth in advertising we should also make it clear that this is not a "get rich quick" book. Indeed the Efficient Market Hypothesis, to which we subscribe with some qualifications, implies that there is no royal road to riches in the financial markets: their secret is that there is no secret. We believe that studying our work will have a positive payoff, though perhaps more in income from employment than in capital gains. Thanks in part to the infusion of economics, the financial sector has grown rapidly in recent years, and our intention is to help those who wish to participate in its further growth. This book has its origin in an undergraduate lecture course entitled "Securities, Options and Futures" that Houthakker taught once a year starting in 1980. Designed as an elective for economics majors, the course consistently attracted a sizable enrollment, which suggests that it filled a need. Its purpose was to make students with a background in microeconomics and macroeconomics—but with only modest knowledge of mathematics—aware of the light shed by the theoretical contributions just mentioned on the financial markets. Since there was no book that covered all these topics on a suitable level, Williamson transformed the notes taken by Robert Jones in the early 1980s into a preliminary text, adding much new material in the process. This text went through many revisions and extensions. We are grateful to a succession of teaching fellows—especially to Bruce Darringer, Stephen Grenadier, Jennifer van Heeckeren, Gordon Phillips, Judith Ruud, and Eduard Sprokholt—for helpful suggestions and to Herbert Addison of the Oxford University Press for his encouragement and patience. The first author also has learned much from his colleagues on the board of the New York Futures Exchange, particularly from John Phelan and Lewis Horowitz. Harvard University INSEAD, The European Institute of Business Administration November 1995

H.S.H. P.J.W.

Contents

1 Introduction

3

1.1 What This Book Is About 3 1.2 Financial Markets and Financial Instruments Defined 1.3 Basic Concepts of Accounting 9 1.3.1 The Balance Sheet 10 1.3.2 The Cash Flow Statement 12 1.3.3 The Income Statement 14 1.4 Sources of Information 15 2 The Place of Financial Markets in the Economy

7

16

2.1 Real Assets and Financial Claims 16 2.7.7 Balance Sheets for the U.S. Economy 19 2.1.2 The International Investment Position of the United States 21 2.1.3 The Distribution of Financial Assets 22 2.2 A Framework for Macroeconomic Analysis of Flows 23 2.2.7 The National Accounts 24 2.2.2 The Flow of Funds Accounts 28 2.2.3 The Relation between Stocks and Flows 30 2.2.4 International Transactions 31 2.2.5 Exchange Rates 32

viii

CONTENTS

2.3 The Rate of Interest 35 2.3.1 The Rate of Interest in a Barter Economy 35 2.3.2 Government Borrowing 36 2.3.3 Introducing Money: Nominal and Real Interest Rates 37 2.4 Monetary and Fiscal Policy 40 2.4.1 The Supply of Money 40 2.4.2 The Demand for Money 43 2.4.3 The Objectives of Monetary Policy 45 2.4.4 Fiscal Policy and the Government Budget 46 3 The Supply of Securities

48

3.1 General Characteristics of Securities 49 3.2 The Supply of Government Securities 49 3.2.1 Federal Government Obligations 50 3.2.2 Municipal Bonds 52 3.2.3 Bonds of Foreign Governments and International Organizations 53 3.2.4 Index-Linked Bonds 53 3.3 Corporate Financial Policy 54 3.3.1 Empirical Evidence 59 3.4 The Supply of Corporate Securities 61 3.4.1 Corporate Equities 62 3.4.2 Corporate Takeovers 67 3.4.3 Corporate Bonds 67 3.4.4 Junk Bonds 68 3.4.5 Convertible Securities 69 3.4.6 Partnership Units and Business Taxation 70 3.5 Mutual Fund Shares 71 3.5.1 Money Market Funds 74 3.6 Mortgages and Mortgage-Backed Securities 74 3.7 Claims on Financial Institutions 75 4 The Demand for Securities

78

4.1 The Time Dimension 79 4.1.1 A Case in Microeconomics: Saving for Retirement 79 4.1.2 Present Value and Duration 81

CONTENTS

IX

4.1.3 The Calculation of Yields on Zero-Coupon Bonds 87 4.1.4 The Term Structure of Interest Rates 88 4.2 The Risk Dimension 90 4.2.1 The Measurement of Risk 90 4.2.2 Bivariate Distributions 93 4.2.3 Expected Utility 95 4.2.4 Estimating the Mean and Variance of Returns 103 4.2.5 Conditional Probabilities and Expected Values 104 4.3 The Portfolio Complication 105 5 Securities Markets and Their Efficiency

110

5.1 Central Trading Places 111 5.1.1 Stock Exchanges 111 5.1.2 Types of Orders and Their Execution 116 5.1.3 Specialists and Market Clearing 118 5.2 Financial Markets without Central Trading Places 122 5.2.7 The Over-the-Counter Stock Market 123 5.3 Stock Exchanges in Other Countries 125 5.3.1 The International Stock Exchange in London 126 5.3.2 The Tokyo Stock Exchange 129 5.4 Operational Efficiency and the Efficient Market Hypothesis 130 5.4.1 The Weak Form of the EMH, and Technical Analysis 132 5.4.2 Do Equity Prices Follow a Random Walk? 135 5.4.3 The Semistrong Form of the EMH, and Security Analysis 137 5.4.4 How Rapidly Do Prices Adjust to News? 138 5.4.5 The Strong Form of the EMH 139 5.4.6 Conclusions on Informational Efficiency 140 6 The Determination of Equity Prices

141

6.1 Shares as Claims to Future Dividends 142 6.1.1 Steady Growth in the Dividend 142 6.1.2 Aggregate Dividends, Earnings, and Inflation 6.1.2 Aggregate Dividends, Earnings, and Inflation 145145 6.2 Shares as Claims to Corporate Net Worth 146 6.3 The Capital Asset Pricing Model 150 6.3.1 The Simplest Form of CAPM 151

*

CONTENTS

6.3.2 Extending the CAPM 156 6.3.3 Estimating Betas 158 6.3.4 Implications for Portfolio Management 159 6.3.5 The Validity of CAPM 162 6.4 Arbitrage Pricing Theory: An Alternative Approach 162 6.5 Appendix: Stock Indexes 164 6.5.1 The Three Main Indexes 164 6.5.2 Some Other Stock Indexes 167 7 Security Analysis

168

7.1 Security Analysis and Market Efficiency 168 7.2 A Modern View of Security Analysis 169 7.2.1 Macroeconomic Developments and Changes in Regime 170 7.2.2 Industry Growth 171 7.2.3 International and Regional Growth 175 7.2.4 Industry Structure 177 7.2.5 Firm-Specific Factors 180 7.3 The Role of Financial Statement Analysis 182 7.3.7 The Adjustment Process of Financial Ratios 186 7.3.2 Pro-Forma Income and Cash Flow 188 7.3.3 Caterpillar Inc.: A Security Analysis and Valuation Example 191 7.4 Shortcuts in Security Valuation 195 7.4.1 Uses and Pitfalls of Price/Earnings Ratios 196 7.4.2 Tobin's q as an Alternative Approach to Securities Valuation 198 8 Options and Options Pricing

201

8.1 The Basics of Stock Options 202 8.7.7 Institutional Aspects: Exchange-Traded Stock Options 202 8.1.2 The Payoff from Buying and Selling Options 205 8.1.3 Combinations of Options 207 8.1.4 Combining Options with Stocks 209 8.1.5 The Put-Call Parity Theorem 211

CONTENTS

XI

8.2 The Valuation of Stock Options 213 8.2.1 The Expected Payoff of a European Call 215 8.2.2 Application of the Capital Assets Pricing Model to Options 216 8.2.3 The Black-Scholes Formula for a European Call 217 8.2.4 Alternative Derivations of the Black-Scholes Formula 220 8.2.5 Other Option Models 222 8.2.6 Some Extensions of the European Call Formula 223 8.2.7 The Empirical Relevance of the Black-Scholes Formula 226 8.3 Options and Portfolio Management 226 8.4 Convertible Bonds and Stocks as Options 227 8.5 Other Types of Options 229 9 Futures Contracts and Futures Markets

230

9.1 Forward Contracts 231 9.2 The Origins of Futures Trading 232 9.3 Basic Elements of Futures Contracts 234 9.3.1 Delivery and Cash Settlement 235 9.3.2 Futures and Options 238 9.4 The Organization of Futures Markets 240 9.4.1 Categories of Traders 242 9.4.2 Types of Commodities and Financial Instruments Traded 244 9.4.3 Volume and Open Interest 246 9.5 Appendix: The Euromarkets and the Swap Market 251 9.A.I Innovations in Euromarket Instruments 252 9.A.2 The Swap Market 253 10 Futures Prices

255

10.1 Profits and Losses on Various Transactions 256 10.1.1 Implied Limits on Simultaneous Price DifferencesDifferences 257 257 10.2 Relations among Spot and Futures Prices 258 10.2.1 Financial Futures 258

XII

CONTENTS

10.2.2 Nonseasonal Commodities 263 10.2.3 Seasonal Commodities 265 10.3 Hedgers, Speculators, and Market Equilibrium 268 10.3.1 A Portfolio Analysis of Hedging 269 10.3.2 Hedging Effectiveness 10.3.2 Hedging Effectiveness 271271 10.3.3 Market Equilibrium 272 10.4 The Role of Expectations 273 10.4.1 Futures Prices as Predictors of Spot Prices 274 10.4.2 Expectations versus Spot-Market Constraints 274 10.4.3 Samuelson's Conjecture on Increasing Volatility 276 10.5 Futures and Portfolio Management 278 10.5.1 Program Trading 278 10.5.2 Portfolio Insurance: A Post-mortem 279 10.5.3 Futures Contracts as an Investment 280 11 Regulation of Financial Markets

283

11.1 The Ethics of Finance and the Economic Function of Financial Markets 283 11.2 The Purposes of Regulation 285 77.2.1 Maintaining Competition 285 11.2.2 Preventing Fraud and Providing Information 11.2.2 Preventing Fraud and Providing Information 286286 11.3 Levels of Regulation 287 11.4 Federal Regulation of Trading in Corporate Securities 288 11.4.1 Reporting of Financial Results and Other Developments 288 11.4.2 New Issues 289 11.4.3 Insider Trading 290 11.5 Federal Regulation of Futures Markets 290 11.6 A Case Study: The Silver Manipulation of 1979-1980 292 11.6.1 The Silver Market 292 11.6.2 The Manipulation 293 11.6.3 The End of the Manipulation 295 11.6.4 The Other Side of the Story 296 11.6.5 The Aftermath 297 11.6.6 Regulatory Aspects 297 11.7 Regulation in the United Kingdom 299

Xiii

CONTENTS

Notes

303

Bibliography

335

Author Index

349

Subject Index

351




1 Introduction

1.1 WHAT THIS BOOK IS ABOUT

When you pick up a copy of the Wall Street Journal or London's leading financial daily, the Financial Times, you see only the tip of an iceberg. Underneath lie the millions of individual transactions that move the prices of different financial instruments, create and destroy fortunes, spawn new instruments, and retire old ones. It is relatively easy to discover what has happened as a result of all this activity. In fact, with the help of electronics many of us can watch it happening minute by minute. But have you ever asked, how is this change happening, and why? Take a look at the newspaper headlines from a typical working day and try it: • General Motors Corp. reported a fourth quarter loss of $651.8 billion and a world record-breaking $23.5 billion deficit for the year. Investors boosted the company's stock to $40.50, up $1.25 per share, or 3%. • Schering-Plough, the U.S. drugs and health care company, has authorized the repurchase of an additional $500 million of its common shares. The news prompted Moody's Investors Service, the U.S. rating agency, to cut the group's long-term debt ratings. • The opening of trading in Eastman Kodak was delayed due to an early imbalance on the sell side. • Inflation slide sends equities forward. • Depressed dividend yield on stocks no longer seen as a warning sign. • Tokyo—The Nikkei closed moderately higher. Traders said prices moved forward just before the close in technical trading linked to options activity. • London—News of better than expected public debt repayment figures

3

4

INTRODUCTION

prompted switching to long-dated paper and a flattening of the yield curve. • Chicago—Prices of near-term grain and soybean futures ended nearly unchanged on Monday, but more distant wheat deliveries rose. • New York—A burst of program trading lifts equity prices toward the close. • Washington—The Federal Reserve Bank of New York attributed a rash of squeezes in the Treasury bond market in 1992 primarily to natural forces. This book examines and explains many of the processes at work behind these types of headlines. It discusses in detail each of the main financial markets; those in equities (also called shares or stocks), bonds, foreign currencies, options, and futures contracts. We examine the variety of objects being traded (known collectively as financial instruments), the pricing of these instruments, and the types of transactions occurring in each market. Some of our discussion is primarily descriptive, helping the reader master the jargon of financial markets and understand the different institutional players. Throughout this book, however, we draw on economic analysis to explain not only "what" and "how" but also "why." Take the example of news of lower inflation producing a rally in the stock market. In Chapter 2 we deal with the crucial first link in this chain of events. We examine the way in which macroeconomic developments, such as changes in Gross Domestic Product (GDP) growth or inflation, influence the supply and demand for financial assets and the price of money (i.e., its nominal and real interest rate). We also outline the ways in which government fiscal and monetary policies impact the financial markets, an increasingly important topic given the pervasive influence of large government budget deficits in the United States and many other countries. Consider the Schering-Plough repurchase of $500 million worth of its common shares. This action changes the supply of its securities on the market. Because of the interrelationships between the securities supplied by a single issuer, the announcement of a share repurchase also influenced the opinion of Moody's (a rating agency) on the Schering-Plough bonds already outstanding. These are aspects of the supply side of the securities markets discussed in Chapter 3. There we explore the characteristics and relative importance of different securities including government securities, municipal bonds, corporate equities and senior debt, junk bonds, convertibles, mutual fund shares, and claims on financial institutions, as well as the ways in which the supply of each changes over time. The supply of securities also changes when a government repays some of its national debt. However, the fact that, according to the Financial Times, such a repayment by the British government prompted switching to longer-dated paper also reflected the behavior of demand from investors. This demand side of the financial markets is the topic of Chapter 4. Three important factors driving demand are covered in detail: the time value of money, attitudes toward risk, and

WHAT THIS BOOK IS ABOUT

5

the possibility of reducing risk by holding a diversified portfolio of investments. Economic analysis plays a central role in helping us progress beyond vague notions of investor attitudes to a more quantitative approach to demand behavior. This approach allows us to develop the links between demand and interest rates on bonds of different maturities or rates of return on financial instruments with different risk profiles. The financial markets discussed in this book are generally highly competitive: Information flows rapidly and different volumes of instruments can change hands more or less continuously with little friction. But the efficiency and smooth working of these markets is not an accident; their structures and procedures have been designed to achieve these goals. Even then they sometimes temporarily fail. In the Wall Street Journal quotation about the delayed opening of trading in Eastman Kodak shares, the market for these shares was suffering from a bout of indigestion that had to be remedied. In Chapter 5 we explain how the New York Stock Exchange (NYSE) and some of the world's other most important markets for securities work to promote smooth and efficient trading. Equally important, we analyze the implications of the way financial markets operate for the kinds of information that are likely to be rewarded with higher profits. After all, one won't get rich by telling the market what it already knows. Having discussed the supply and demand for securities and the organization of the financial markets in which they are exchanged, we then tackle the issue of security prices in Chapter 6. We begin with one of the largest and best-known categories of financial instruments: equities. What is the relationship between the dividends paid and expected by holders of a stock and its price on the exchange? Why might it be that the Wall Street Journal observed: "Depressed dividend yields no longer seen as a warning sign"? How does the market price of a stock with a particular risk and expected return vary with the return expected on others? To answer these kinds of questions we call again on economic analysis. From the previous list of newspaper headlines, General Motors reported worldrecord losses but its share price rose by 3%. This rise may have reflected expectations among a majority of investors that the company's results would shortly improve. But how might one go about analyzing whether the majority's sentiments are correct? How much is GM's stock really worth on the basis of the cash and profits it is likely to generate in the future? Techniques of security analysis designed to help answer these questions are the subject of Chapter 7. We begin by examining the implications of market efficiency for the possible returns to be gained from security analysis. We explain how to analyze the intrinsic value of a corporate equity taking into account the responsiveness of the company's performance to economic growth, the structure of its industry, and its sources of competitive advantage. The insights to be gained by proper analysis of a company's financial statements are explained. Finally we assess the uses and pitfalls of various shortcuts to security valuation including the uses of priceearnings ratios and Tobin's q ratio.

6

INTRODUCTION

The report that "the prices of stocks in Tokyo rose because of technical trading linked to options activity" is just one example of the important role that options now play in the world's financial markets. As we discuss in Chapter 8, options contracts have long been a familiar part of everyday life. When you guarantee a hotel reservation against a credit card, you are actually buying a form of option. But it is only recently that options have come to be widely traded as financial instruments. We discuss the most important types of option contracts now available and the possibilities for creating an even wider range of different investment positions by combining various options contracts or mixing options and equities. Some of the main models for valuing options are presented, and we explore the lessons of options theory for valuing convertible bonds and stocks themselves. Terms such as March soybean futures and even stock index futures refer to a part of the financial markets that remains a mystery even to many investors who have long traded actively in stocks and bonds. But during the 1980s a number of futures markets, especially financial futures, grew much faster than other types of securities trading. In the United States, financial futures trading alone now involves well over 100 million contracts per year. Futures contracts are a class of instruments that no serious student or practitioner of the financial markets can afford to ignore. In Chapter 9 we explain the basic elements of a futures contract and the terminology used to describe the different futures positions and their relationship to the underlying assets. We then discuss the organization of futures markets and the different categories of traders. How futures are priced and their relationship to the current market price (known as the spot price) is covered in Chapter 10. We explore different determinants of prices of both commodity futures (contracts based on a tangible commodity) and financial futures (those based on another financial instrument or index). After looking at the role of futures in "program trading" and the realities of so-called portfolio insurance through the use of futures and options—a concept that was put to the test by the "Black Monday" crash of 1987—we conclude by discussing futures as an investment. When investment performance is mediocre, more than one investor or analyst has probably dreamt of creating a "squeeze" or even of "cornering" a financial market so as to exercise monopoly power in what are usually highly competitive markets. In an operation that was later described as "beyond greed," a syndicate of investors in the silver markets tried to do just that. Distortions caused by artificial squeezes or corners can force legitimate investors and speculators into unfair bankruptcy, undermine confidence in the trading system, and destroy its liquidity. In these cases regulation is called for to maintain fair competition and efficiency in the financial markets. At the same time, the authorities must avoid cumbersome regulations that would hamper legitimate trading or close markets unnecessarily. As the final headline from the list illustrates, there can be debate about whether certain market behavior is a "natural" consequence of healthy competition or reflects attempts by a few parties to control the market

FINANCIAL MARKETS AND FINANCIAL INSTRUMENTS DEFINED

7

for their advantage. Likewise, there are questions as to whether or not particular trading rules would achieve their ultimate objectives even if followed to the letter. Nonetheless, regulation, which also serves to diminish the risk of fraud, is a daily fact of life for participants in financial markets. In Chapter 11 we therefore discuss how the regulatory processes work, what they have set out to achieve, and how well they have performed. Starting from a macroeconomic perspective on the financial markets, each successive chapter therefore fills in a piece of the jigsaw puzzle: the drivers of supply and demand for financial instruments; how these forces come together to determine the prices of stocks and bonds; the operation of securities markets both in the United States and across the globe; and the opportunities to improve investment returns through security analysis. We then examine the increasingly important markets for options and futures. We describe how these markets work and analyze the forces determining prices and generating profits and losses for the different players involved. We hope that the reader who finishes this book and then picks up the Wall Street Journal or the Financial Times will be able to look beyond the headlines to assess the real implications of each story with the help of economic analysis. Our purpose does not end there, however. The financial markets provide an abundance of object lessons for those with some training in economics. Not the least of the markets' fascinations is that they are constantly being innovated and thus challenge the insight of those who follow them, whether from the inside or the outside. In many countries, in fact, the financial markets are among the most dynamic sectors of the economy.

1.2 FINANCIAL MARKETS AND FINANCIAL INSTRUMENTS DEFINED

In its original meaning, a market is a small area, say a city square or a specially designated building, where buyers and sellers gather. Names such as Haymarket Square in Boston recall this history. A market in this narrow sense is herein referred to as a central trading place. In economics the word market usually has a wider meaning. We speak, for instance, of the U.S. labor market, yet there is no single place where employers and workers get together to conclude employment contracts. Similarly we speak of the capital market as if it were a single market, though in fact it consists of a large number of submarkets, each dealing with particular financial instruments and often without a central trading place. This book is mostly concerned with markets in the narrow, historical sense. The stock exchanges and the futures markets are important examples; in both the physical proximity of buyers and sellers (possibly represented by middlemen) is essential to the trading process. We only refer occasionally to such abstract notions as the capital market as a whole.

8

INTRODUCTION

The discussion, however, is not confined to central trading places such as the New York Stock Exchange and the Chicago Board of Trade. There are other important financial markets (notably those in government bonds, in foreign currencies, and in over-the-counter stocks) that do not have central trading places yet share many features with markets in the narrow sense. In the markets just mentioned, buyers and sellers do not gather in one spot, but they keep in constant touch by telephone, telex, and other devices. Competition in these spatially dispersed markets can be just as intense as in those with central trading places, and it is the intensity of competition that really matters. Financial markets are accordingly defined as highly competitive markets in financial instruments. By financial instruments we mean readily negotiable claims. A bond is a claim on the interest and principal promised by the issuer of the bond. A share in a corporation is a claim on any dividends that the corporation may pay in the future, and on the residual value in case it is liquidated. A futures contract (defined in Chapter 9; see also Chapter 10) is a claim on certain quantities of the commodity or security underlying the contract. An option (discussed in Chapter 8) is also a claim, but the buyer does not have to exercise it. Since futures and options differ in essential ways from equities and bonds, and are traded in different markets, they may be called derived financial instruments, or derivatives for short. In accordance with common usage, the term security is reserved for equities, bonds, and certain similar financial instruments (discussed in Chapter 3). In this book, therefore, we deal with three broad classes of financial instruments: securities (particularly equities and bonds of various types; see Chapters 3-7), options, and futures. In our definition of financial instruments, ready negotiability means that the owner of the claim in question can sell it without undue delay at a price that is close to the price at which he or she could buy the same claim. It is important to note that a highly competitive market is not one in which there is a single price for every item traded.1 On the contrary, in such a market—and also in many less competitive markets—there are normally two prices: the bid price, at which someone is willing to buy the item, and the offer price (or asking price), at which someone is willing to sell it.2 The difference between the bid price and the offer price is known as the bid-ask spread. A small bid-ask spread is the hallmark of a highly competitive market; thus we see that the definitions of financial markets and of financial instruments are mirror images of each other. What constitutes a "small" bid-ask spread is somewhat arbitrary; a spread of less than 1% may be considered small, but a spread of 5% or more certainly is not. The bid-ask spread is not the only component of the cost of buying and selling. In addition, there are usually commissions and other fees payable by the buyer and/or seller. Both buyer and seller may spend some of their time on the transaction. For a market to be highly competitive, these other costs, which need not be the same for all participants, must also be small. By no means do all claims satisfy the criterion of ready negotiability. If you

BASIC CONCEPTS OF ACCOUNTING

9

have lent money to your destitute cousin, you may have a hard time finding someone willing to buy this claim at face value (or anywhere near it), so it is not a financial instrument in the sense used in this book. Many corporate shares are not readily negotiable, either; in the United States there are literally millions of corporations,3 but no more than about 6,000 different shares are regularly traded on stock exchanges and other competitive markets. Your corner drugstore, or even your doctor, may well be a corporation, but there is no ready market for their shares. Corporations of this type are sometimes described as closely held; typically the stockholders (if there is more than one) all belong to one family. Such corporations are generally small, though a few are in the billion-dollar range. In the aggregate, closely held corporations account for a large part of the corporate sector, but since trading in their shares is infrequent at best, we are mostly concerned with listed firms, whose shares are traded in competitive markets, particularly the stock exchanges and the over-the-counter market.

1.3 BASIC CONCEPTS OF ACCOUNTING

In the study of financial markets one of the main tools is accounting, including both private and national accounting. A full treatment of this subject is beyond the scope of this book, but a brief discussion is needed to grasp the economic meaning (or lack of it) of accounting statements, which are all too often accepted at face value.* In the equity markets, for instance, much attention is paid to corporate earnings, yet it will be shown that published earnings reports can be quite misleading. To understand accounting it is first of all necessary to distinguish between stocks and flows.4 A factory building or a retail store is a stock because it does not depend on the units (days, years, etc.) in which time is measured. The value of the store, for example, could be $1 million, not $1 million per week. A firm's sales and profits, by contrast, are flows; to be meaningful they must be expressed in terms of a time interval, such as a quarter or a year. Thus a firm may have sales of $10 million per year. In accounting, therefore, we find two kinds of statements: stock statements and flow statements. The only stock statement needed for present purposes is the balance sheet, which will be discussed first; after that we shall consider two kinds of flow statements: the cash flow statement and the income statement. In this section all stock and flow statements are assumed to refer to firms. These statements can also be used for individuals, and indeed you may find it instructive to calculate them for yourself. In Chapter 2 we provide accounting statements for various aggregates such as an entire country or the corporate sector of an economy. * Parts of this section will be familiar to readers with previous knowledge of accounting, but they may find it worthwhile to at least skim through it.

10

INTRODUCTION

1.3.1 The Balance Sheet

The balance sheet of a firm may be thought of as a snapshot showing its financial condition at a certain point of time. Another important distinction must now be made, namely between assets and liabilities. Assets are what the firm owns, liabilities are what it owes. The difference between a firm's total assets and its total liabilities is its net worth, also called the value of the firm. A simplified example of a firm's balance sheet is presented in Table 1.1. The categories listed under assets and liabilities are typical for a manufacturing firm and do not call for comment at this point. Some of the dollar figures attached to these categories, however, need a closer look. The most straightforward item is Cash, which includes currency and readily available deposits at banks. Its money value is obvious, provided the currency and deposits actually exist—a question to be decided by the firm's auditors. Other uncontroversial items are Accounts Payable (that is, payable to the firm's suppliers) and Bank Loans. The only comment relevant to Accounts Receivable (from the firm's customers) is that some adjustment must be made for claims that may be uncollectable. For Land and Plant and Equipment, more difficult problems emerge. Recall that the purpose of a balance sheet is to shed light on the value of the firm, which may be defined more precisely as the amount a buyer would pay for the firm as a whole. Suppose the firm owns a parcel of land that cost $25 million when it was acquired 20 years ago but is now worth $50 million.5 Which of these figures should be used on the balance sheet? To an economist the answer Table 1.1 Balance Sheet as of the End of 1993

and 1994 (millions of dollars)

ASSETS Cash Accounts Receivable Land Plant and Equipment Inventories TOTAL ASSETS

LIABILITIELIABILITIESS

Bank Loans Accounts Payable Mortgages and Bonds TOTAL LIABILITIES NET WORTH

1993

1994

75 200 150 600 150

95 190 150 620 130

1175

1185

300 100 550 950

200 150 530 880

225

305


11

is clear: a potential buyer of the firm would not be interested in the historical cost of the land but only in its current value of $50 million. Nevertheless, that is not what would be entered on the balance sheet published by most firms with the approval of their auditors; there we would find the land valued at its historical cost of $25 million. Thus we encounter a major obstacle in interpreting conventional accounting, which has its own rules and is only remotely connected with economics. A firm's auditors will not approve its balance sheet and other financial statements unless they agree with Generally Accepted Accounting Principles (GAAP). These principles are primarily designed to prevent fraud, not to provide economic insight. This is why they stress easily ascertainable facts, such as historical cost, and frown upon the estimates often needed to use current values. The full implications of GAAP become clearer in the context of the profit-and-loss statement discussed in the next subsection. In the meantime, it should be made clear that the statements used as examples in this section are all assumed to satisfy GAAP. Returning to Table 1.1, consider further the category of assets, Plant and Equipment. The buildings, machinery, and vehicles in this category gradually lose their usefulness because of wear and tear, obsolescence, and exposure to the weather until they can no longer be used profitably. Although some of these effects can be offset by maintenance and repairs, it is usually necessary to set aside funds for replacement. This procedure is called depreciation and will affect the balance sheet figure. The general rule is that the balance sheet should show the depreciated value of plant and equipment. How much is set aside for depreciation will again depend on the method of accounting. Under GAAP a truck that originally cost $30,000 and has an expected life of 5 years should be depreciated in such a way that after 5 years only the salvage value (if any) appears on the balance sheet.6 The difficulty with this approach is that after 5 years, due to inflation and other factors, trucks may cost more than they did initially, so that the accumulated depreciation will not be sufficient to trade in the old truck for a new one. It would clearly be more prudent to calculate depreciation on the basis of replacement cost instead of historical cost. Whenever the current cost of an asset rises, depreciation would then be increased to provide enough money for ultimate replacement; in the rare cases where the current cost falls over time— computers are a case in point—depreciation could be reduced. When discussing the income statements some further ramifications of changes in current cost will be pointed out. (see Section 1.3.3). The final category of assets is Inventories, which usually consist of raw materials (to be used as inputs in future production), finished (but as yet unsold) products, and work in progress (such as a ship under construction, provided it is still owned by the shipbuilder). Raw materials, in particular, are subject to considerable price fluctuation, and once more it is the current cost that matters from the economic point of view, whereas GAAP would normally stick to the historical cost.7

12

INTRODUCTION

On the liabilities side, the only item remaining for discussion is Mortgages and Bonds. Under GAAP they would be shown at face value, which is normally the amount to be repaid when they are due. However, if the bonds are traded in the market, as they are likely to be for sizable corporations, their prices will vary over time. It could be argued that bonds should be valued at the market price if it is less than the face value, since the debtor could buy back the bonds at that price. Since corporations do not often trade in their own bonds, and since entering them at less than face value might raise doubts about the debtor's commitment to repay them in full, there is a case for not valuing bonds at market prices. To complete the discussion of Table 1.1 a few words should be said about net worth. On an actual balance sheet for a corporation net worth is often broken down further into the nominal value of the shares and a remainder called surplus. This breakdown is not very meaningful because the surplus also belongs to the shareholders; in any case the nominal value (also called par value) of a share has little economic significance because corporate shares, unlike bonds, cannot be redeemed at this value.8 The final question we must ask about Table 1.1 is whether it really gives an adequate picture of the firm's value in the sense defined earlier. We have seen that it may not do so under GAAP, but is replacement cost accounting the whole answer? In general it is not because it does not include some important items that a potential buyer of the firm would consider. One of these is technology, especially if it is supported by patents. Although the value of patents is sometimes difficult to estimate, they certainly have to be recognized if they are present. An even more shadowy item is "goodwill," which represents the firm's success in establishing steady relations with its customers by advertising and the like. It is clear, for instance, that such brand names as Coca-Cola and Macintosh give their respective firms a value beyond the tangible assets and liabilities included in the table. For simplicity's sake, however, these "intangible" assets are not shown here. 1.3.2 The Cash Flow Statement

We now proceed to the flow statements, the most straightforward of which is the cash flow statement. As the name implies, it represents inflows and outflows of cash and these can be determined unambiguously. In some corporate reports this statement appears under the heading "Sources and Uses of Funds." The principal distinction made in Table 1.2 is between current items and capital items. Current items affect the balance sheet only through the cash balance, whereas capital items affect the specific assets and liabilities directly.9 Apart from this distinction, it must be borne in mind that all items are shown as inflows and outflows of cash, regardless of their economic interpretation. A few comments on the entries in the table may be helpful. The first current item, Sales, refers to sales of output produced during the year, not to sales from


13

Table 1.2 Cash Flow Statement for the Year 1994 (millions of dollars) CURRENT ITEMS 1 Sales 2 Cost of Goods Sold

3 GROSS OPERATING PROFIT (1+2) 4 Overhead Expenses 5 Interest Paid

6 Research & Development

7 8 9 10 11

NET OPERATING PROFIT BEFORE TAX (3+4 + 5 + 6)

Taxes Paid (less refunds) NET OPERATING PROFIT AFTER TAX (7 + 8)

Dividends Paid

4000 -3000 1000 -250

-80 -50 620 -300

320 -100

NET CURRENT CASH FLOW (9+10)

220

CAPITAL ITEMS 12 Net Purchases of Land 13 Net Purchases of Plant and Equipment 14 Change in Inventories

0 --80 20

15

NET PURCHASES OF REAL ASSETS (12+13+14)

16 17 18 19

Net Net Net Net

Increase in Accounts Payable Decrease in Accounts Receivable Increase in Bank Loans Increase in Mortgages and Bonds

-60

50 10 —100 --20

20

NET CHANGE IN CLAIMS AND LIABILITIES (16+17+18 + 19)

-60

21

Net Issue of Equities

-80

22 23

NET CASH FLOW IN FINANCIAL ITEMS (20+21) NET CASH FLOW IN ALL CAPITAL ITEMS (15 + 22)

24

NET TOTAL CASH FLOW (11+22)

--140 -200 20

preexisting inventories or to sales of assets and securities. The Cost of Goods Sold represents expenses specifically related to the production of particular products, such as the wages of production workers, raw materials, and consumption of energy. Overhead Expenses include the salaries of managers and other employees (for instance secretaries and janitors) whose work is not attributable to particular products; it may also include advertising. The Interest Paid is obviously related to the bank loans, mortgages, and bonds encountered on the balance sheet.10 Among the capital items, Net Purchases of Plant and Equipment refers to investment in new buildings, machinery, and so on, less the proceeds of any such assets that were sold. The Change in Inventories gives rise to a positive cash flow if inventories are reduced and to a negative flow if they are increased; as mentioned earlier, changes in inventories are not included in the current item "sales." A Net Increase in Accounts Payable, if positive, is a source of funds and hence a positive cash flow, and the same is true of a Net Decrease in Accounts Receivable. As regards Net Issue of Equities, this clearly results in a

14

INTRODUCTION

Table 1.3 Income Statement for the Year 1994 (millions of dollars) 1 Net Operating Profit before Taxa 2 Depreciationb 3

INCOME BEFORE TAX (1--2)

5

INCOME AFTER TAX (3--4)

4 Taxes Paid (net of refunds)c 6 Dividentsd 7 Retained Earnings (5—6)

620 60 560 300 260 100 160

a

Cash flow item 7.

b

On plant and equipment.

c

Cash flow item 8.

d

Cash flow item 10.

positive cash flow if it is positive; in Table 1.2, however, it is negative and therefore corresponds to net purchases by the firm of its own shares. 1.3.3 The Income Statement

While the cash flow statement may be viewed as the core of a firm's system of accounts, it does not cover everything. Thus the attentive reader will have noticed the absence of depreciation, which is not a cash item. Moreover, the cashflow statement is not what actual or potential shareholders are primarily interested in.11 Their first concern is likely to be the Income statement, which does include depreciation but otherwise is derived from the cash flow statement. An example of an income statement is given in Table 1.3, which should be selfexplanatory. Recall at this point that all statements are assumed to be on a historical cost basis. The difficulties this causes for depreciation have already been discussed in Section 1.3.1. We saw there that, in an inflationary environment, depreciation according to GAAP is likely to fall short of what is required to keep capital intact.12 Replacement cost accounting actually has further consequences for the income statement that cannot be pursued here in detail: if assets are revalued in line with current prices there will be capital gains (or, more rarely, losses) for which additional lines are needed on the income statement. This will become clearer in Chapter 2, where we discuss aggregate accounting (see especially Section 2.2.3). To conclude the section on accounting, it is necessary to deal briefly with the relation between the balance sheet and the two flow statements. Taking Plant and Equipment as an example, we see on the balance sheet a value of $600 million for the end of 1993 and of $620 million for the end of 1994; the difference represents net purchases of $80 million (line 13 of the cash-flow statement) less depreciation of $60 million (line 2 of the income statement). The differences

SOURCES OF INFORMATION

15

Table 1.4 Reconciliation of the Income Statement with the Balance Sheets (millions of dollars) 1

NET WORTH AT END OF 1993

225

2 Retained Earnings in 1994 3 Net Issue of Equities in 1994

160 -80

4

305

NET WORTH AT END OF 1994 (1+2 + 3)

in cash between the two balance sheets agree with the final item of the cash flow statement. A reconciliation of net worth is given in Table 1.4, which shows that (at least under GAAP) changes in net worth can be reduced to two factors: retained earnings and net issue of equities. The reader is encouraged to verify why, in the final analysis, only these two factors matter.

1.4 SOURCES OF INFORMATION

There are abundant sources of information on the financial markets. Every day the Wall Street Journal and the better general newspapers contain pages and pages of data. Those who need still more can sometimes find additional facts in the Investor's Business Daily or, for international markets, in the Financial Times. Newspapers are not very convenient for research purposes, and market data in machine-readable form can be obtained from the Center for Research in Security Prices (known more crisply as CRISP) at the University of Chicago and from a number of private firms. The principal stock and futures exchanges also publish detailed statistical yearbooks. In addition to reference books such as Moody's Industrials, Compustat is the main source of machine-readable financial data on listed corporations. The very abundance of financial data is itself a problem; to make sense of them one needs theories, several of which can be found in later chapters of this book and in numerous other texts on finance or investments. There are also many books of the "get-rich-quick" variety; the frugal shopper can often pick these up on the remainder tables for a dollar or less, which is approximately what they are worth. No doubt fortunes can be made in the financial markets, but those who have succeeded are rarely if ever able to explain how they did it.

2

The Place of Financial Markets in the Economy

In this chapter we deploy some of the frameworks and concepts of macroeconomics to explore the place of financial markets in the economy. We also introduce a few important questions, such as how interest rates are determined, that are elaborated upon in later chapters. One of the main tools of analysis is provided by the National Income and Product Accounts (NIPA), which extend the accounting concepts developed in Chapter 1 to the economy as a whole. These accounts are combined with the Flow of Funds accounts into a framework for describing supply and demand in the securities markets. We then use this framework to discuss the effects of monetary and fiscal policy and of inflation, particularly on interest rates. 2.1 REAL ASSETS AND FINANCIAL CLAIMS

Anyone who has observed the response of the financial markets to rumors concerning changes in the monetary policy of the Federal Reserve Board, and to news of unexpected changes in Gross Domestic Product or inflation, will appreciate the importance of understanding the influence of macroeconomic developments on the pricing of securities. Conversely, large changes in share prices (such as occurred on "Black Monday" in October, 1987) often raise concern about their possible effect on the economy at large. The purpose of this and the following sections is, therefore, to outline a framework for describing the interrelations between changes in overall economic activity, monetary and fiscal policy, and shifts in the international balance of payments on the one hand, and security prices on the other hand. We begin with some basic notions of capital, saving, and real capital formation. Underlying the operation of any economy is a stock of real (as distinct from 16

REAL ASSETS AND FINANCIAL CLAIMS

17

financial) capital in the form of land and natural resources, buildings, inventories, productive equipment, consumer durables, and public infrastructure such as highways and schools. In addition to these tangible assets there are various "intangible" (but nonetheless real) assets, specifically human capital and the organizational systems built up by firms,1 governments, and nonprofit entities in the course of their past activities. In some cases these assets represent direct saving and investment by those who employ them, such as the homeowner's equity in his or her dwelling or a farmer's investment in the fertility of his land. More commonly, however, an asset embodies the savings of individuals other than those who employ that asset directly; these savings are made available to owners of real assets through the credit mechanism, of which the financial markets are a major component. Examples include the home partly purchased with mortgage funds and the plant and equipment employed by a corporation and financed by equities and various forms of debt. By relying on credit, households and firms can acquire assets without waiting until they have accumulated all the funds needed to buy them. In any economy based on private property, therefore, the existence of a productive asset is frequently associated with some form of credit: There is a financial liability on the part of the owner and a financial claim elsewhere in the economy. The specifics of the financial contracts that relate the credit to the assets will depend on the nature of the service generated by the asset, its productive life, and other factors. There will consequently be many kinds of financial contracts differing in their risk, return, and maturity characteristics (see Chapter 3). If these contracts are financial instruments, as defined in Chapter 1, they will be traded in financial markets. The ownership of shares in a corporation does not constitute credit in the strict sense of the word, but it gives rise to financial instruments that are readily negotiable in the case of the larger corporations and are similar in most respects to instruments arising from credit. The broad pattern of real assets and financial claims underlying a country's economy is set out in Table 2.1. Each column represents the aggregate portfolio of real assets and liabilities held by the individual entities that make up a major economic sector. The coverage of three of these sectors (households, nonfinancial business, and government) is clear, but the other two require a word of explanation. The private financial sector includes banks, savings institutions, pension funds, insurance companies, security brokers and dealers, consumer finance companies, mutual funds, and money market funds. The foreign sector, sometimes described as the "Rest of the World," enters to the extent that it has assets in or liabilities to the country concerned. In general, financial claims are not listed if the corresponding liabilities are within the same sector; in other words, only "net" claims appear in the table. At any instant in time, each sector, as well as the economy as a whole, must satisfy the basic balance sheet identity: Real Assets + Financial Assets = Liabilities + Net Worth.

18

THE PLACE OF FINANCIAL MARKETS IN THE ECONOMY

Table 2.1 The Structure of Assets (+) and Liabilities (--) Personala

Businessb

Financec

Government

ROW*

Net

+ + + 0 + 0 + +

+ + 0 + + 0 0 +

+

+

+

0

+

0

+ + + + + + +

Goldf Currency Bank deposits Pension fPension Pension fundsg fundsg +undsg + Mortgages Consumer loans Equitiesh Business loans

0 + + ++ + + — + +

GovernmentGovernment Government bondsibondsi bo Unpaid taxesi Bank reserves Net claims on ROWd

+

+

_

0 + /-

REAL ASSETS

Lande Dwellings Consumer durables Business fixed assets Inventories Public infrastructure Human capital Other intangibles

0

0

0

=

0

0 0 0

+ + 0

0 0

+

+

0

0

+

0 +

+ +

0 0 0

+

FINANCIAL ASSETS AND LIABILITIES

Corporate bonds

NET WORTH

+

+

+ +

+ -

-

-

-

+

+

+ +

.+

-

+ -/ + 0 0 0

+

+

-/+

+

+

_

_

-

0

+

-

-

0

+ -

+ 0 0

+/-

+/-

+/-

-/+

0

0

+/-

+/-

0 0 0 0 0 0 0 0 0 0 0 0 0

+

a

Households, personal trusts, and private nonprofit institutions.

b

Nonfinancial only. Private only; the monetary authorities and federally sponsored agencies are considered part of the government.

c

d

Rest of the World.

e

Includes natural resources. f Including official reserves of foreign exchange and claims on the International Monetary Fund and similar organizations. g Including life insurance; in both cases the reserves of these financial institutions are considered to belong to the ultimate beneficiaries. h Including equity in unincorporated business. i

Including treasury bills and other short-term obligations. Less refunds, normally less than taxes due.

j

The business and financial sectors are considered to belong to their ultimate owners: the shareholders in the case of corporations, and the proprietors or partners in the case of unincorporated firms. Consequently these two sectors are shown with zero net worth in Table 2.1.2 Among the private sectors, only households have a positive net worth. In principle one could also argue that the government belongs to the people, but for various reasons that idea is difficult to


19

implement statistically. Since the government debt normally exceeds the value of its tangible and financial assets, it appears with a negative net worth, while the debt itself shows up as an asset of the household sector. The net worth of the Rest of the World reflects the balance of foreign claims and liabilities, and may be of either sign. Finally it will be noticed that although the financial items (unlike the real assets) always add up to zero, this is true only because the Rest of the World is included as a sector. As the reader can easily verify, the net worth of the country as a whole equals the value of its real assets plus its net claims (which may be negative) on the Rest of the World. These net international claims are discussed in Section 2.1.2. 2.1.1 Balance Sheets for the U.S. Economy

The ideas expressed in Table 2.1 have to a large extent been implemented by the Federal Reserve Board in a publication with the same title as this section.3 Drawing in part on estimates from the U.S. Department of Commerce, the Board has assembled data on the tangible assets of three private sectors (households, nonfinancial business, and private financial institutions) and combined these with its existing statistics on the stock of financial assets and liabilities. Although incomplete—intangible assets are missing, and so are the government sector and the Rest of the World—the result is an illuminating overview of the U.S. economy. A condensation of these data for the end of 1993 is presented as Table 2.2. Tangible assets (except land and inventories) are valued at their current cost (essentially the same as replacement cost)—that is, what it would cost at that time to produce exactly the same assets—rather than the historical cost at which they were originally produced. As shown in Chapter 1, from the economic point of view historical cost belongs to the category of bygones that are bygones. Nevertheless it should be realized that these values could not be obtained by adding the corresponding items on the balance sheets published by individual firms, which generally reflect historical cost.4 Land, inventories, and financial claims are in principle valued at their market price, though this may not be true for all items. Looking first at private tangible assets, you see that in the household sector real estate accounted for more than half of the total.5 In the business sector land and plant and equipment were the largest items; the dwellings listed there are typically apartment buildings. Private financial institutions owned relatively few tangible assets. Among the financial claims, money, which includes savings deposits and the like, accounted for about one-third of the net financial assets of households. Not surprisingly, money so defined was also a large liability of the financial sector. Another important category of financial assets in the household sector was its equity in noncorporate business, although it was not as large as the market value of corporate equities held by that sector. The two equity items together accounted for about one-quarter of household net worth.6 Claims on pension funds and life insurance companies were also a large household asset;

20


these institutions invest mostly in corporate and federal securities, in mortgages, and, to a lesser extent, in commercial real estate. The household sector owned few corporate bonds, which were largely held by financial institutions. Although its holdings of government securities were still relatively minor, they increased rapidly in recent years because of favorable yields on the long-term issues. Table 2.2 Assets and Liabilities of Major Private Sectors, End of 1993 (trillions of dollars) Personal"

Businessb

Financialc

2.9 4.3 2.3

0.5j

1.2 1.4 4.7 1.1

0.1 0.0 0.5 0.0

10.0

8.4

0.6

0.8

-3.8 -5.1

TANGIBLE ASSETS Landd Dwellings Consumer durables Plant and eqipment Inventories TOTAL NET FINANCIAL ASSETS AND LIABILITIES Moneye

Pension fundsf fundsf Mortgages Corporate equities Other equityg Corporate bondsh Government securities Miscellaneous itemsi TOTAL NET WORTH

3.1 5.4 -2.8 4.1*

2.4 0.2 1.1

-0.1 -1.1 0.0i 0.0l -1.2

0.1

2.2

1.8m 0.0l

1.0 3.6 1.0

-0.4 13.1

-0.5 -2.1l

0.7l

23.0

6.3l

1.3l

a

Households, personal trusts, and private nonprofit organizations.

b

Nonfinancial only; includes farms and unincorporated business.

c

Private only; includes mutual funds.

d

Includes natural resources.

"Including all types of bank deposits and money market funds f

Including life insurance; the reserves of pension funds and life insurance companies are considered to belong to the ultimate beneficiaries. g

Equity in unincorporated business.

h

Including commercial paper and foreign bonds.

i

Including consumer, trade and security credit, and bank loans.

j

Owned by private nonprofit organizations.

k

At market value. Includes all mutual funds (including bond funds).

l

Equity in the sector's own firms is not deducted as a liability.

m

Represents the sector's holdings of corporate equities less the value of mutual fund shares. Preceding footnote also applies. Source: Board of Governors of the Federal Reserve System, Balance Sheets for the U.S. Economy 1945-93, September 1994.


21

Both households and business had considerable net liabilities in the form of mortgages. Some of these mortgages were held by government agencies such as the Federal Housing Administration. Since the government is not included in Table 2.2 because the data are incomplete, mortgage liabilities are less than the mortgage assets shown. It should also be borne in mind that the rest of the world is omitted as well. The treatment of corporate and noncorporate equities in Table 2.2, which differs from that in Table 2.1, needs some explanation. These equities appear as an asset of the household sector but not as a liability of the other two private sectors. The reason is that the net worth of a corporation, as shown in Chapter 1, is the difference between its total assets and its total liabilities to third parties; thus the table indicates a total net worth of the business and financial sectors of $7.6 trillion ($7.6t for short), compared to equity holdings (of households and financial institutions) valued at $4. It. 7 This means, in effect, that the market valued business assets at less than their reproduction cost.8 To sidestep this problem, equity is not considered a liability of the business and financial sectors. The total net worth of the three private sectors, therefore, cannot be obtained simply by adding the figures in the bottom row of the table. In fact there is no unique answer to this question. If the market is assumed to value business assets correctly and the government is ignored, then total private net worth is equal to the net worth of the personal sector.9 If reproduction cost is used as the valuation method, then the market value of corporate equities should be deducted from the stated net worth of the business and financial sectors, and the three net worth figures can then be summed to give total private net worth on a consolidated basis; an adjustment for foreign shareholdings is also needed. As a final observation, the exclusion of the government sector from Table 2.2 has important consequences. Among the assets of the three private sectors are government securities, but the corresponding liability does not appear. Barro (1974), in an influential article entitled "Are Government Bonds Net Wealth?", has persuasively answered his own question in the negative. His basic reason is that government obligations represent future tax liabilities of which prudent individuals should take account in calculating their net worth. This does not necessarily mean that these obligations should be deducted in toto from private net worth, since the government also has considerable assets. There are no official estimates of the value of government assets, so the government's net worth is uncertain. We have to recognize that the national net worth is unknown and that it is not the same as the private net worth. 2.1.2 The International Investment Position of the United States

Both business and government have long been involved in the rest of the world, but the extent of their involvement has increased greatly in recent years. Until the early 1980s the United States had net claims on the rest of the world, which

22


Table 2.3

U.S. and Foreign Assets Outstanding (billions of dollars, end of year)

1980

1985

1990

FOREIGN ASSETS OWNED BY U.S. RESIDENTS

673

884

1390

of which: Direct investment abroad Corporate equities and bonds

404 68

425 225

U.S. ASSETS OWNED BY FOREIGNERS

394

769

of which: U.S. government securities Corporate equities and bonds Direct investment in United States

136 56 126

241 252 231

502 439 468

743 613 517

U.S. NET FOREIGN ASSETS

279

115

-267

-633

633 225 1657

1993 1497

716 501 2129

Source: Board of Governors of the Federal Reserve System, Balance Sheets for the U.S. Economy 1945-93, September 20, 1994.

meant that the value of foreign assets held by U.S. residents (including the government) exceeded the value of U.S. assets held by foreigners. As Table 2.3 shows, there has been a drastic change in recent years. Although U.S.-owned foreign assets increased significantly, foreign-owned U.S. assets increased much more, and the net asset position of the United States with respect to the rest of the world became strongly negative. The value of foreign-held corporate equities and corporate bonds rose more than tenfold between 1980 and 1990, much more than the percentage increase in U.S. holdings of foreign corporate securities. The same pattern is found in direct investment. Foreign holdings of U.S. government securities also rose substantially. The trends in assets shown in Table 2.3 are to a large extent a reflection of the trends in the balance of payments discussed in Section 2.2.4. To put the negative net asset position of the United States in perspective, it should be compared with the net worth figures of Table 2.2. At the end of 1993 that position amounts to less than 3% of household net worth, hardly an alarming ratio. What is disturbing about the figures in Table 2.3 is not so much the present situation as the rapidity with which it has deteriorated: In the course of 13 years the United States changed from the world's large creditor to the world's largest debtor. More to the point in this book, however, is the observation that through their holdings of American government and corporate securities foreigners have become a major presence in American financial markets, just as American investors have long been in foreign markets. 2.1.3 The Distribution of Financial Assets

It is also interesting to know that, assuming there were about 93.5 million households at the end of 1993, the average net worth per household was about

FRAMEWORK FOR MACROECONOMIC ANALYSIS OF FLOWS

23

$190,000. Needless to say the distribution underlying this average was very unequal.10 A handful of households owned as much as a billion dollars each, while a great many had zero or negative net worth.11 Moreover the bulk of the households with positive net worth had most of their assets in the form of real estate and pension claims, rather than in financial instruments as defined earlier. The ownership of financial instruments, in fact, is concentrated among the wealthy. In 1976, the latest year for which such estimates are available, the wealthiest 1% of all persons in the United States held 18% of all assets, but they held 46% of the corporate stock, 30% of the bonds, and 37% of other debt instruments. On the other hand, they owned only 13% of the real estate, 11% of the cash, and 7% of the life insurance. Among the assets held by the top 1%, corporate stock accounted for 29% of the total, as compared to 11% for the population at large.12 More recent data, though not entirely comparable to those just cited, shed further light on the distribution of financial asset holdings. In 1984, according to a government survey, only 20% of all households owned stocks and mutual fund shares, but this fraction was as high as 66% for households whose net worth exceeded $500,000 and 49% for households with monthly incomes over $4,000.13 Among households with a monthly income below $2,000, only 10% owned shares. The distribution of interest-earning assets such as bonds and money market funds (but excluding checking accounts) was similarly unequal. These statistics may suggest that in the United States the idea of "people's capitalism," according to which most of the population would be directly involved in the major financial markets, is far from being realized.14 It should be remembered, however, that many people who do not own stocks or bonds directly nevertheless have an indirect interest through pension funds or life insurance policies that are invested in those instruments.

2.2 A FRAMEWORK FOR MACROECONOMIC ANALYSIS OF FLOWS

So far we have looked at balance sheets, which give a snapshot of the situation on a particular date. The assets and liabilities on these balance sheets are in a continual state of flux because, among other things: • The monetary authorities alter the supply of money • The government sector runs a surplus or a deficit, thus changing the supply of government obligations • New capital is created • Most existing capital assets—land is an exception—depreciate • New types of claims are introduced15 • The population and the labor force change in size and composition • Various changes occur in the rest of the world

24


• The nonfinancial sectors adjust their balance sheets according to economic conditions These portfolio adjustments in turn determine the supply and demand for securities and are therefore essential to the study of financial markets. To understand these changes you need to look at the flows, as distinct form the stocks, in an economy. This distinction is ultimately based on a similar one in microeconomic accounting (particularly of business firms), where the balance sheet covers stocks and the profit-and-loss statement covers flows. 2.2.1 The National Accounts

The best-known system of macroeconomic flow statistics is the National Accounts (known officially as the National Income and Product Accounts, or NIPAs), with which the reader is assumed to have at least a nodding acquaintance. Recall that the National Accounts present two main aggregates: 1. Gross Domestic Product,16 which is the market value of all goods and services produced during a period; it is divided into four components: private consumption expenditures, gross private domestic investment, government purchases of goods and services, and net exports. GDP is available not only in current prices but also in constant prices (that is, with an adjustment for inflation); in the latter form it provides the most comprehensive measure of economic activity. 2. National Income, which is the sum of all factor payments (wages and salaries, dividends, profits of unincorporated enterprises, interest, and rent). Of special importance to the financial markets are the National Accounts data on saving and investment. The economic function of these markets is, among other things, to help channel savings into profitable use (particularly in capital formation) and to help finance capital formation by attracting savings. "Investment," in the national accounting context, is the formation of real capital, not the buying of financial instruments; in fact, financial instruments as such do not appear in these accounts. Since this dual meaning of the word "investment" is a source of confusion, we occasionally use the term "(real) capital formation" where appropriate, but it is difficult to do so consistently because national accounting terminology is widely used. The NIPAs assume that investment, in the sense of capital formation, is undertaken only by the business sector.17 The meaning of saving in the NIPAs depends on the sector where it occurs: • In the household sector saving is simply the difference between personal income after taxes and consumers' outlays. • The profits of unincorporated business firms (partnerships and sole proprietorships) are attributed to the households that own them, and the only savings of this sector are therefore the amount these firms set aside for the


25

replacement of their capital assets, known technically as capital consumption allowances. • In the corporate business sector, saving equals retained earnings (that is, income after dividends and taxes) plus capital consumption allowances, which are called "depreciation" in Chapter 1. • For the government sector (including state and local), saving—negative in recent years—is the difference between current receipts (mostly taxes) and expenditures (purchases of goods and services plus transfer payments). • From the U.S. point of view, saving by the rest of the world equals net U.S. imports of goods and services.18 For recent years the flow of saving and investment in the United States is summarized in Table 2.4. Note that the business sector does the bulk of the gross saving, mostly in the form of capital consumption allowances. During the middle 1980s, the savings of the household sector were more than offset by the dissaving of the federal government, and this was also true in 1993. As a perTable 2.4 Gross U.S. Saving and Investment (billions of dollars) 1980

1985

1990

1993

Personala Noncorporate business: Depreciation* Corporate business: Depreciation* Undistributed profits

137

125

170

193

122

169

235

261

181 38

269 103

394 63

437 91

Gross private saving Government: Federal State and local

478

665

861

1003d

-61 27

-197

65

-164 25

-241

445 16.3

534 15.6

723 16.1

708 13.8

Gross private domestic investment Net foreign investment

437 13

643 -114

809 -79

882 -92

GROSS INVESTMENT

450 16.5

529 13.2

730 13.2

790 12.5

5

-5

8

2

GROSS SAVING

as % of National Income

as % of GDPC

Statistical discrepancy

26

a

Households, personal trusts, and nonprofit organizations.

b c

Includes the capital consumption adjustment. Undistributed profits include the inventory valuation adjustment.

GNP in 1980 and 1985.

d

Includes wage accruals less disbursements.

Source: Survey of Current Business, July 1994 and earlier issues.

26


centage of National Income, gross saving has not shown any significant trend between 1980 and 1990 despite large federal deficits. Note also that total saving is almost equal to investment; the difference is due to the "statistical discrepancy," which is a (rather inadequate) measure of the inaccuracies in the National Accounts. Total gross investment (including net foreign investment) as a percentage of GNP declined significantly during the 1980s and early 1990s. This decline is often held responsible for the relatively slow increase in productivity in recent years, though it may not be the only cause. Many items in the National Accounts—specifically GDP and its components but not National Income—are published both in current prices and in the prices of some benchmark year (currently 1992, but until recently 1987). This feature provides various price indexes, which are the most comprehensive ones available for the American economy. The simplest of these is known as the GDP deflator, calculated by dividing GDP at constant prices into GDP at current prices. Another is the GDP fixed-weight price index; it is considered more meaningful than the deflator because the latter is influenced by changes in the relative importance of consumption, capital formation, and the other components of GDP. In view of the central importance of inflation in the analysis of security prices we present a chart of the annual rate of inflation measured by percentage changes in the index or deflator. Figure 2.1 shows not only the GNP deflator19 but also the more familiar Consumer Price Index (CPI) for urban consumers. Five principal conclusions can be drawn from Figure 2.1: 1. Without exception, inflation has been positive since 1960 (and also, we may add, in nearly all earlier years since World War II). 2. Inflation has been quite variable throughout the period shown. 3. The two most recent peaks in inflation were associated with the "oil shocks" of 1973-1974 and 1979; similarly, the dip in 1986 reflected a temporary collapse of the price of crude oil. 4. In the early 1990s inflation came close to the low rate prevailing in the early 1960s. 5. There is not much difference between changes in the GDP deflator and changes in the CPI, but the latter, which covers only part of GDP, is distinctly more volatile. 6. Changes in the CPI tend to precede changes in the deflator by a short time interval. 7. Economic theories of inflation will be discussed in Section 2.4.1. The growth rate of the economy is at least as important as the inflation rate because of its effects on the welfare of consumers and on the profitability of firms. It is also closely watched by participants in the financial markets, though perhaps more because of its presumed impact on inflation than for its own sake.20 Customarily measured by the percentage change in GDP at constant prices, it is made public every quarter, with monthly revisions as more of the underlying data become available. Although these quarterly numbers are indis-


Figure 2.1

27

Two measures of inflation. Source: Data from Economic Report of the President, February 1995, tables B-3 and B-63.

pensable in assessing short-run developments in the economy, we shall consider only changes from year to year. The solid line in Figure 2.2 shows the annual growth rate of real GDP from 1960 through 1992. The well-known pattern of booms lasting several years, punctuated by shorter recessions, is clearly discernible. The 1970s stand out as a very disturbed period, as they did in the preceding chart. Economic performance in the 1980s was much better—in fact the boom of that decade was the longest on record—but the following recovery has gathered considerable strength. On the average, growth since 1960 has been around 3%. Figure 2.2 also shows changes in the related concept of "output per hour" (that is, GDP per hour worked in the business sector of the economy), often referred to as "productivity". This is actually a rather loose use of the term; productivity is more properly defined as the ratio of output to the aggregate of all inputs, whereas output per hour (OPH) reflects only labor inputs without adjustment for the quality of labor.21 Despite this defect, output per hour is of interest because it clarifies fluctuations in growth rates to some extent. Changes in OPH tend to "lead" changes in GDP. Typically, OPH increases markedly at the end of a recession, when firms are able to produce more output without hiring more labor. During booms the growth of OPH tends to decline as employment rises strongly while output rises at an approximately constant rate. Therefore, OPH is worth watching as a predictor of future GDP. Although we cannot show it here, a rise in OPH may also have a favorable effect on inflation and corporate profits.

28


Figure 2.2

Annual growth rates of real GDP and of output per hour. Source: Data from Economic Report of the President, January 1993, tables B-1 and B-45; updated from Economic Indicators, August 1993.

2.2.2 The Flow of Funds Accounts

Another system of macroeconomic flow statistics, the Flow of Funds (FOF) accounts, is particularly oriented toward financial institutions and markets, so it is directly relevant to our subject matter. Published quarterly by the Federal Reserve Board, these accounts shed light on the linkages between macroeconomic trends and the securities markets. While relying on the National Accounts for macroeconomic data, the Flow of Funds contains a great deal of additional information, some of which provides a check on the National Accounts. Originally this system was designed as a matrix (that is, a table arranged in rows and columns) describing the financial flows between different sectors of the economy.22 The present usefulness of the Flow of Funds resides less in the matrix than in the more detailed tables covering particular sectors and particular types of financial instruments (see Chapter 3). By way of introduction we give another example in Table 2.5; it refers to the household sector and provides further perspective on personal saving. The table has two main parts, gross saving and gross investment. The first part includes net saving (that is, gross saving less depreciation), the concept most economists have in mind when they talk about saving without further clarification. The NIPA concept of personal saving, encountered in the preceding section, also refers to net savings. Both the National Accounts and the Flow of Funds derive net saving as the difference between disposable income and consumption. In the Flow of

29


Table 2.5

Saving and Investment of the Personal Sectora (billions of dollars)

Disposable personal income -Personal outlays* = Personal saving (NIPA)C + Adjustments to incomed + Net durablese = Net saving (Flow of Funds) + Capital consumptionf = GROSS SAVING GROSS INVESTMENT

Capital expendituresg residential construction consumer durables Net acquisition of financial assets deposits at financial inst.h U.S. govt. securities other fixed interesti mutual fund shares other corporate equities pension fundsj noncorporate equity miscellaneous assets Net increase in liabilities home mortgages other liabilities Statistical discrepancyk

1980

1985

1990

1993

1994

1918 1781

2943 2754

4051 3881

4689 4496

4960 4756

137 35 33 206 244 450

190 73 96 358 340 697

170 92 90 352 494 846

193 110 89 392 583 974

204 116 100 420 634

448 343 113 219

743 538 162 353 527 125

1067

-13

33 5 1 -11

-111

935 697 192 468 465 72 127 30 38 -22

-77 12 128 96 32

282 -59 52 321 161 154

-28 57 227 179 48

990 809 250 538 497 -21 5 -6 187 -33 344 -10 31 316 178 138

-6

-46

-89

-16

233 153

119

15

147 76

191

1054

898 261 591 526 44

359 19

77 -89 134 -45 27 357 186 171

a

Includes nonprofit organizations.

b

Personal consumption expenditures plus interest paid by consumers to business and net personal transfers to foreigners (from the National Accounts).

c

Correspondsto the first line of Table 2.4.

d

Credits from government insurance.

e

Expenditures on consumer durables less depreciation.

f

Depreciation of dwellings, durables, and nonprofit capital goods.

g

Net of sales. Includes capital expenditures of nonprofit organizations.

h

Includes currency.

i

Includes municipal and corporate bonds as well as montgages.

j

Includes the increase in life insurance reserves.

k

Gross saving minus gross investment.

Source: Federal Reserve, Release Z.1, March 8, 1995.

Funds, however, income and consumption are defined somewhat differently; as a result, the FOF estimate of saving varies from the NIPA estimate. As to income, the FOF increases it by an item (capital gain dividends) that

30


is not found in the NIPAs at all.23 Although not large in relation to income, this item is sizable in relation to saving. The difference between the two agencies in the treatment of consumption is more important both conceptually and quantitatively. The FOF considers consumers' expenditure on durable goods to be investment (in the sense of capital formation). This view requires an allowance for depreciation on the stock of durables. Unlike the National Accounts, moreover, the FOF keeps owner-occupied dwellings in the household sector, thus avoiding the artifact of treating homeowners as businessmen who pay rent to themselves. The end result of all this is that the Flow of Funds usually conies up with higher—sometimes much higher—estimates for net saving than do the National Accounts. In recent years there has been much concern about the decline in the personal savings rate (the ratio of net saving to disposable personal income), but in the FOF there is little evidence of such a decline.24 So much for net saving. Nothing further needs to be said about gross saving, which corresponds to the funds available from the household sector for investment. The most distinctive contribution of the Flow of Funds is in the gross investment part of Table 2.5, where we see what the sector did with the available funds. Most of these went into real capital formation (dwellings and durables). The remainder was used for net acquisition of financial assets and is of particular interest for the analysis of financial markets. Note, for instance, that households were net sellers of corporate equities other than mutual funds during the years shown in the table, as indeed they have been for the last three decades.25 Household purchases of mutual funds have generally not been large enough to offset these sales of corporate shares. Apart from large increases in bank deposits, households did much of their financial investment through pension funds and life insurance, which in turn (not shown in the table) have, by and large, bought the corporate shares sold by households.26 As noted already, in the last few years the household sector has bought large amounts of U.S. government bonds. Leaving further study of Table 2.5 to the reader, we now tie up a loose end by connecting the balance sheet data of Section 2.2 with the flow data just discussed. This is similar to the reconciliation between the stock and flow data undertaken at the end of the accounting section in Chapter 1. 2.2.3 The Relation between Stocks and Flows

It is clear that data on the stock of assets, such as those in Table 2.2, cannot be independent of data on the flow of the same assets, such as those in Table 2.5. If the household sector held $3.3t of money at the end of 1989 and $3.1t at the end of 1988, then there must have been a flow of $0.2t during 1988. But this conclusion holds only because the price of money is always the same; it need not hold if prices have changed. For any asset other than money, the difference between the beginning and ending stock depends not only on the flow but also on any changes in value that may have occurred during the period. In fact, an accurate allocation of the change in stock into a flow component and a revaluation component would be a virtually impossible task in the case of


31

Table 2.6 Asset Revaluations for the Household Sector (billions of dollars) 1980

1985

1990

1993

91

148 343 28

Dwellings Corporate equities Equity in unincorporated business Pension fund reservesa

143 252 297 40

47 381 98 91

TOTAL REVALUATIONSb

851

654

-168

728

Disposable personal income Total revaluation as % of DPI

1953 44

2943

4051 -4

4689

22

Net worth Total revaluations as % of NW

9666

13938

19059

23027

9

5

-1

3

-111

-25 -82

169

16

a

Includes life insurance.

b

Includes certain assets not listed separately. Excludes land holdings, where the change in value cannot be decomposed into revaluation and net purchases. Also excludes government and corporate bonds, for which no revaluations are calculated. Source: Federal Reserve, Release C.9, September 20, 1994.

equities and other assets whose prices vary incessantly.27 Although any actual allocation must therefore be approximate, the result would still be of interest because it would shed light on the magnitude of capital gains and losses. The main reason for wanting to know about gains and losses is that, according to some theories, consumers' expenditure—the main component of GDP—is affected by them. Let us see, then, what revaluations are implied by statistics such as those in Table 2.2. This is done for the household sector in Table 2.6, for a few major types of assets and for all relevant assets combined; personal disposable income is included for comparison. The table shows that revaluations were quite variable from year to year, both in their total and their composition. The general though irregular rise in equity prices was a major source of capital gains. These capital gains were large enough to have a potential effect on consumption, but such an effect has not been conclusively demonstrated. 2.2.4 International Transactions

As shown in Section 2.1.2, the U.S. economy in general, and the financial markets in particular, have become increasingly integrated into the world economy. It is therefore necessary to pay attention to financial flows to and from the Rest of the World. Table 2.7 shows certain aggregates from the National Accounts. In this table receipts from foreigners are by definition equal to payments to foreigners; this is accomplished by including the balancing item (Net Foreign Investment) in payments to foreigners. It is equivalent to the Balance on Current Account, as it is known in international economics,28 which in turn is defined to be equal (with the opposite sign) to the Balance on Capital Account. The differ-

32


Table 2.7

Summary of International Transactions (billions of dollars) 1980

1985

1990

1993

Merchandise exports Factor income Other services

361 226 81 53

399 222 97 80

726 399 169 158

796 461 137 198

PAYMENTS TO FOREIGNERS Merchandise imports Factor income Other services Transfers (net)

361 249 47 45 9

399 343 82 74 17

726 509 147 120 29

796 592 132 132 32

NET FOREIGN INVESTMENT

12

—118

-79

-92

-121

-110

RECEIPTS FROM FOREIGNERS

Memo: Trade balance Balance on invisibles

-23 33

—16

31

-131 39

Source: Survey of Current Business, July 1994 and earlier July issues.

ence between merchandise exports and merchandise imports is called the trade balance, while the difference between the other components of the Balance on Current Account is sometimes referred to as the balance on invisible items. Neither the current-account nor the capital-account balance can be legitimately regarded as the cause of the other. Thus a country can have a currentaccount deficit—and consequently a capital-account surplus—because its exports do not sell well enough to pay for its imports, but the same pattern can emerge if its securities are more attractive to foreigners than foreign securities are to the country's residents. During the 1980s the U.S. government had to borrow heavily because of a budget deficit. As explained in Section 2.3.2, this tended to make U.S. interest rates high relative to those prevailing in certain other countries, particularly Japan. The Japanese therefore bought large amounts of American government and private securities and acquired the dollars needed to pay for these securities by running a merchandise surplus. No doubt this is not the whole story, but it should be noted that unless a country can finance a budget deficit by private domestic saving, it will necessarily have a current-account deficit.29 In other words, the role of the financial markets in international transactions is not necessarily passive, as popular and official indignation about the Japanese trade surplus tends to assume. One reason the Japanese do not buy as much of our products as we would like is that they buy so much of our securities. 2.2.5

Exchange Rates

To gain further insight into the data in Table 2.7 we must look at the exchange rate of the dollar in terms of other currencies. Since the foreign exchange mar-


Figure 2.3

33

International value of the U.S. dollar (index numbers, March 1973 = 100). Source: Data from Economic Report of the President, February 1995, table B-12.

kets are among the most active financial markets, and since other financial markets (such as the equity markets) are increasingly influenced by developments in exchange rates, a simplified discussion of this complicated subject may be helpful in any case. It is complicated because, as is often the case in economics, everything affects everything else. Instead of attempting a formal analysis, which may be found in any good text on international economics, we shall argue mostly from examples. To begin with, Figure 2.3 presents two measures of the international value of the dollar. There are so many bilateral exchange rates that it is convenient to use index numbers. The particular indexes shown here reflect the weighted value of the dollar in terms of the currencies of ten industrial countries, the weights being based on the trade between the U.S. and each of these countries. The first measure (called "nominal") takes the exchange rates as they are quoted; the second (called "real") includes an adjustment for inflation here and in each other country.30 These indexes are not comprehensive, since they exclude such important trading partners as Mexico and China. Nevertheless they give a more accurate picture than the few bilateral exchange rates—particularly the dollaryen and the dollar-mark rates—that receive most attention in the financial press even though they can be quite misleading. The period covered by Figure 2.3 starts in 1973, when the present regime of floating exchange rates was established. Until 1971 exchange rates were fixed, except for infrequent devaluations or revaluations. After a brief interval of transition, the major countries agreed to let supply and demand determine exchange rates, but they reserved the right to intervene. The present regime can therefore be described as "managed floating."

34


From Figure 2.3 we see considerable variation in the international value of the dollar, but the overall trend was slightly downward.31 This trend is somewhat more pronounced in the real index, indicating that on balance the ten other countries had more inflation than the United States and that the deterioration was not due to excessive inflation here. Let us now try to interpret some of the more conspicuous developments. Exchange rates influence the trade balance through the demand for imports in the country of destination and the supply of exports in the country of origin. Thus if the dollar is expensive in other countries, the demand for American exports is discouraged and so is the supply of exports from the United States. As a result, the American trade balance tends to becomes smaller (or more negative), generally after a delay of one or two years. The demand for imports also depends on the overall level of economic activity in the importing country, as measured by its GDP; when GDP rises (everything else remaining the same), the demand for imports also rises. Some of the service components of the current account behave in a similar manner: when the dollar is down, we see more Japanese tourists in the Harvard yard and fewer Americans on the Eiffel Tower. International movements of capital are sensitive to the rates of return prevailing in different countries. When German securities yield more than British securities, some capital will flow from Britain to Germany, and borrowers (or issuers of equities) will seek funds in Britain rather than in Germany. Such capital movements are to some extent deterred by exchange rate risk, but we shall see in Chapters 9 and 10 that this risk can be hedged. In addition, some capital movements are speculative (that is, they are made in anticipation of a favorable movement in the exchange rate). At times such speculation may involve large sums and force intervention by central banks. An important difference between current-account and capital-account transactions is that the former respond much more slowly to changes in their basic determinants than the latter. Capital moves with little or no delay, but flows of goods and services adjust only with a lag. Since by definition the current-account balance is the opposite of the capital-account balance, the exchange rate has to be at a level that will bring about this equality. Because of the delayed response of the current-account balance, short-run variations in exchange rates are dominated by capital movements. In the longer run the current-account balance has an important effect on exchange rates. Going back to Figure 2.3, we notice a pronounced rise in the dollar index during the first half of the 1980s, followed by an even more pronounced fall in the second half and a much smaller and irregular decline thereafter. The initial appreciation appears to have been due mostly to the rise in U.S. interest rates shown in Figure 2.4. Nominal interest rates increased due to a large budget deficit and a restrictive monetary policy (see Figure 2.5), but this monetary policy also reduced the inflation rate. The net result was that investing in the United States became very attractive, while borrowing here became correspondingly less

THE RATE OF INTEREST

35

attractive. So much capital flowed in that the negative effect on the currentaccount balance was more than offset, at least temporarily, and the external value of the dollar rose. In due course, as shown in Table 2.7, the U.S. current-account balance did adjust to the appreciation of the dollar. It had been positive in 1980, but by 1985 it had become negative. When interest rates receded to more normal levels in the second half of the 1980s, the current-account deficit started to weigh more heavily on the dollar and the preceding appreciation was reversed.32 During the first half of the 1990s the dollar index remained under slight downward pressure, in part because the current account continued to be in deficit. The underlying problem is that private saving in the United States is not large enough to overcome the government deficit, so capital must be attracted from abroad. It could be attracted by offering higher interest rates, but that might jeopardize domestic prosperity. In effect, therefore, the needed foreign capital is attracted by making the dollar cheaper. The perceptive reader may wonder how long such a policy—never stated explicitly—can be sustained. This important question is outside the scope of this book, but we can say that a continuing budget deficit, even if it is modest in relation to GDP, raises a danger of instability in the currency markets. Unless this deficit can be drastically reduced, the best hope of avoiding instability is the improvement in the U.S. current account that the depreciation will sooner or later bring about.

2.3 THE RATE OF INTEREST

So far we have been occupied with a framework that arranges stocks and flows of real and financial assets in a systematic way. At present this framework has little room, however, for the prices of these assets.33 There is no lack of other sources for asset prices; they are used in following chapters as needed, but not here. At this point, rather, we turn to a preliminary theory of asset prices, changing from a largely descriptive approach to a more analytical one that will enable us to deal with macroeconomic issues important to the financial markets. Important issues are rarely simple. Analysis implies dividing complicated issues into more basic problems that may not be of obvious interest in themselves. It is necessary to start by abstracting from certain features of the real world and to reintroduce them at a later stage. 2.3.1 The Rate of Interest in a Barter Economy

We have already shown that there are numerous kinds of financial instruments, discussed fully in the next chapter, but our introduction to asset pricing begins by assuming there is only one, which may be thought of as a medium-term bond. In the simplified economy considered in this section, the firms are not incorpo-

36


rated, so there are no shares. These firms produce two goods: a consumption good bought only by households (called "bread" for short), and a capital good ("ovens") bought only by other firms. There is no money, and hence no scope for monetary policy; instead, the consumption good itself serves as the standard of value. The only bond, therefore, is denominated in bread; it is initially issued at its face value of 100 loaves of bread, and if the interest rate is r%, the owner of each bond is paid r loaves of bread per year until the bond is redeemed at its face value. In this economy, credit is extended by buying and selling the standard bond. The buyers are households, to whom the bonds are a source of income and a device for structuring their consumption optimally over their lifetime. The sellers are firms, who use the bonds to buy the capital good.34 The question is, what determines the rate of interest? To answer this question, let us first look at the firms that issue the bonds in order to buy ovens. They will do so only if the increase in their output resulting from owning an additional oven is worth at least as much, on an annual basis, as the interest they must pay on the bond; in fact, they will issue bonds and buy ovens up to the point where the marginal product of the oven, expressed in terms of bread, equals the rate of interest r. A household that purchases a bond gives up the bread it could consume now in return for a series of interest payments in subsequent years and a lump-sum payment of 100 loaves when the bond is redeemed. It may seem that the higher the rate of interest, the more bonds a household with a given labor income is willing to buy, but that is not necessarily true. For one thing, it becomes increasingly unattractive to sacrifice present consumption for future consumption as the former approaches the subsistence level. More importantly, a household has a finite life, and there is much evidence that this so-called life-cycle consideration has a decisive influence on the desire to save, which is what purchasing a bond amounts to. A higher r means that less needs to be saved now to permit a specified level of consumption in some future period (say, after retirement). The effect of the interest rate on saving, consequently, may theoretically be of either sign, and empirical research has not found it to be significantly different from zero. If so, the demand for bonds in our simplified economy is inelastic35 and the rate of interest is determined exclusively by the marginal productivity of capital. If the marginal productivity is high (that is, if for some reason, such as population growth, firms find themselves short of ovens), r will be high, and conversely.36 This important conclusion, of course, reflects the simplifying assumptions made in this section, but we shall show that it carries over to some extent to more realistic circumstances. 2.3.2 Government Borrowing

Primitive though this economy is, it can also be used to shed some light on the effects of fiscal policy. Suppose a government spends only on its employees,


37

who are paid in bread as are private employees. To avoid unnecessary complications, suppose the government's revenue is derived entirely from lump-sum taxes that do not interfere with any marginal conditions. As long as the government's budget is balanced, its existence does not affect anything said so far. Now suppose the government decides to hire more workers without arranging for additional revenue. It will then have to issue bonds, which are assumed to be just like the bonds already outstanding. What will this do the rate of interest? Firms, as before, sell bonds up to the point where the interest rate equals the marginal productivity of capital. Households buy bonds in accordance with their income. If that income remains unchanged, the number of bonds outstanding would not change either; the interest rate would clearly have to rise so as to make room for the government borrowing, and a corresponding amount of the real capital formation by firms would be "crowded out."37 Actually, the income of the household sector will not remain the same, for two reasons: (1) The interest payments on the new bonds acquired by the sector will be higher than it was on the old bonds that are redeemed; and (2) the hiring of more government employees may increase employment. Depending on the magnitude of these effects, less investment will have to be crowded out. Conceivably, if unemployment were large enough to start with, no investment would be crowded out at all, and the government borrowing would not lead to any increase in interest rates. To put it in a different way, there will be crowding out of real capital formation only if there is crowding out of labor. The preceding analysis may seem straightforward, but it has been questioned on the ground that a bond-financed government deficit must sooner or later be repaid from increased tax revenues, and that taxpayers will consequently save more in anticipation of these future taxes. If so, no additional employment would be created and the interest rate would not move.38 Since there does not appear to be much empirical support for this objection, we mention it only because it is sometimes comes up in current debates over the large federal deficit in the United States. 2.3.3 Introducing Money: Nominal and Real Interest Rates

When money is introduced into the barter economy just discussed, it is no longer necessary to limit the number of goods. It remains convenient to assume there is only one bond (sold by firms and bought by households), but that bond is now denominated and pays interest in money. The main difficulty created by monetization is that the value of money in terms of goods (or its reciprocal, the general price level) need not be constant. The question where the money comes from is left aside until later; all that needs to be assumed at this point is the existence of some degree of uncertainty about the future value of money. Given this uncertainty, borrowers and lenders will learn to distinguish between the nominal interest rate, expressed in money terms, and the real rate, expressed in terms of the goods they buy or sell. When there is inflation, the

38


nominal rate will exceed the real rate, which is the one that matters to them; indeed, the real rate can easily be negative if inflation is severe enough. Borrowers know that if inflation continues the principal and interest they must pay will represent less in terms of real goods and services; even if they had to increase their total dollar payments, they would still find the entire transaction (borrowing to invest in the capital good) worth their while. Competition will then force them to pay a real interest rate equal to the marginal productivity of capital. Lenders are in a slightly different position. No doubt they would like to be compensated for the loss of purchasing power on each dollar they receive back, but under the assumptions made earlier their supply of bonds is interest-inelastic as long as the interest rate (which now must mean the real rate) is positive. They must therefore rely on competition among borrowers to obtain the real rate. It is also clear that what matters is the inflation expected to prevail until the financial instrument is liquidated: When the loan is repaid, the uncertainty about the value of the principal is removed. If the instrument has a short life (say, one month), there will not be much uncertainty about the value of money since the rate of inflation rarely changes drastically from one month to the next. An allowance for inflation should still be made, but it will not be as uncertain as in the case of long-term bonds where those involved have to estimate the rate of inflation over the next 20 or 30 years. This line of reasoning leads to the following relationship between interest rates and inflation, essentially as first proposed by Irving Fisher in his Theory of Interest: i=r+1e.

In words: the nominal (observed) interest rate i equals the underlying real rate r (based, under our current assumptions, on the marginal productivity of capital) plus the expected rate of inflation le from the present to the redemption of the loan. The last term represents an allowance for the expected decline in purchasing power of the dollars in which the loan is repaid. The subscript in le reminds us that the future rate of inflation is unknown, so it is the expected rate that matters. The assumptions underlying Fisher's theorem are much more general than the highly special ones we have maintained so far. In particular, the theorem does not require that there is only one bond, no equities, and no meaningful government, so we abandon these assumptions at this point. This will make it possible to make some remarks about the performance of Fisher's theorem in the real world. For this purpose it is desirable and customary to eliminate one troublesome feature of the equation, namely the reference to expectations. While theoretically relevant, expectations are difficult to measure and they make the theorem into something of a tautology. It is more interesting to know whether in retrospect nominal interest rates have reflected actual inflation in the way envisaged by Fisher.


39

One test is to compare countries with different inflation rates. In the late 1980s Germany had inflation rates close to zero; the United States, Canada, and the United Kingdom had moderate inflation (say, around 5% per year), while much higher inflation rates were found in certain developing countries, particularly in South America.39 On the whole, interest rates, to the extent they can be made comparable, are in agreement with this pattern: The implied real rates are much less different than the nominal rates. Another test involves comparison of nominal interest rates on medium-term bonds over time for a single country. Historically, the real rate of interest after allowance for actual inflation has averaged in the range of 2% to 4% per annum. Inflation in the United States, meanwhile, has ranged between --1% and +13% per annum since the end of the Korean War. According to Fisher's equation, nominal interest rates should adjust to reflect the sum of the two. Interestingly, however, if we plot the real return investors in a highly liquid, default- free security such as U.S. Treasury bonds actually received over the past 40 years (see Figure 2.4), we observe substantial variation, from real rates that are markedly negative (generally in periods of high inflation) to positive real rates significantly greater than 1 % or 2% (usually during periods of low inflation or deflation). The high real rates of the 1980s may also be linked to the large federal deficit, in accordance with the argument of the previous section.

Figure 2.4 Nominal and real interest rates. Note: Both interest rates refer to a (notional) Treasury bond with a constant maturity of 10 years.The rate of inflation, not shown separately, is measured by the December-to-December change in the Consumer Price Index. Source: Data from Economic Report of the President, February 1995, tables B-63 and B-72.

40


To sum up: While the Fisher equation explains a sizable part of the correlation between nominal interest rates and inflation, significant departures from it do occur, largely because nominal rates seem to be relatively insensitive to shortterm variations in the inflation rate. Part of the explanation of this phenomenon may be that inflationary expectations, an important theoretical determinant of nominal interest rates, respond to changes in the actual rate of inflation only after a substantial lag. Another part may be that the real rate is not constant because of changes in the marginal productivity of capital, also in accordance with the theoretical model.40 All this needs further investigation, but on balance it appears that the Fisher equation needs to be taken seriously. It is of special importance in understanding monetary policy, the subject of the next section. Finally, we emphasize that the Fisher equation applies only to debt, such as bonds and mortgages. It does not apply to equities, which represent ownership rather than debt. The main reason, more fully developed in Chapter 6, is that in the aggregate dividends tend to be roughly proportional to nominal National Income, thus providing a more or less automatic adjustment for inflation. 2.4 MONETARY AND FISCAL POLICY

We are now ready to take up some macroeconomic issues that are of great concern to the financial markets. The first of these is the effect of monetary policy, one of the two principal methods by which the government tries to affect the state of the economy. In the United States, monetary policy is entrusted to the Board of Governors of the Federal Reserve System.41 Actually, basic decisions on monetary policy are made every three weeks by the Open Market Committee, which consists of the seven governors of the system together with the presidents of five of the twelve regional Federal Reserve banks. Since the Committee does not disclose its decisions immediately, much speculation in the financial markets centers on what it has decided or will decide in the future. Sometimes the Committee authorizes the Board or its chairman to make policy adjustments between meetings. 2.4.1 The Supply of Money

The main business of the Federal Reserve is to control the growth of the money stock. The terms "money stock" and its synonym "money supply" are often used loosely, and a list of definitions is needed at this point: • The monetary base equals currency outside banks plus commercial banks' demand deposits at the Federal Reserve. • Ml equals the monetary base plus demand deposits at commercial banks, travelers' checks, and other checkable deposits. • M2 equals M1 plus savings and small time deposits, shares in most money market funds,42 and certain short-term financial instruments.

MONETARY AND FISCAL POLICY

41

• M3 equals M2 plus large time deposits and certain other short-term instruments. • L equals all liquid assets, including M3, Treasury bills, savings bonds, and commercial paper. The Open Market Committee periodically sets target ranges for the growth rate of these concepts and for a related concept, total private debt. The announced ranges for 1985, for instance, included 4% to 7% per year for Ml, 6% to 9% for M2, and 6% to 9.5% for M3. More recently, target ranges for Ml have not been set. In reality, however, it is difficult enough to keep one of these concepts within its range, let alone two or more at the same time.43 When there is a conflict, the Federal Reserve has in recent years tended to give priority to M2. Why is the money stock important? This question, discussed more fully in the following text, goes to the heart of recent controversies in macroeconomics. The Keynesians, who dominated policy discussion until some 20 years ago, held that the money supply served only to determine interest rates, and that interest rates did not matter much outside the financial sector. The Fed's task, in their view, was confined to controlling interest rates. The monetarists, on the other hand, considered the money stock to be the main determinant of nominal GDP (that is, GDP without adjustment for inflation). In an influential book, Friedman and Schwartz (1963) showed that historically there had been a fairly close correlation between M2 and GNP. Later Andersen and Jordan (1968) and Sims (1972) demonstrated that the direction of causality did in fact go from the money stock to GNP, not the other way around as some Keynesians had argued. These researchers also showed that fiscal policy had much less effect on GNP than Keynesian analysis predicted. To illustrate the Friedman--Schwartz findings, using recent data, Figure 2.5 presents percentage changes in M2 and in domestic final sales.44 The change in M2 refers to the year preceding the one to which the other variables refers; thus the change in M2 from 1988 to 1989 is related to the change in domestic final sales from 1989 to 1990. This means that the money supply affects domestic demand with a sizable lag.45 Figure 2.5 shows a high correlation between the two variables in the first half of the period covered. It is also clear, however, that during the 1980s the correlation became much weaker. The monetarist relation based on M2 may be in need of reconsideration; however, a recent study by Feldstein and Stock (1994) tends to support Friedman's theory.46 It is interesting to note that in the early 1990s, when the economy recovered from a recession despite very slow growth in M2, there was a considerable increase in M1. Keynesians and monetarists also differ in their explanation of inflation. Most Keynesians relate inflation to such "real" factors as the unemployment rate and other indicators of idle productive capacity. According to that view, embodied in the "Phillips curve," the general price level will rise in proportion to the strain

42


Figure 2.5 Annual percentage changes in M2 and in domestic final sales, 1960-1994. Source: Calculated from Economic Report of the President, February 1995, tables B-1 and B-68.

that aggregate demand puts on the economy's capacity to produce. They also attribute much importance to developments in particular commodities such as oil and grains. Monetarists, by contrast, emphasize that inflation cannot continue for any length of time without an increase in the money supply, since firms and households would otherwise find themselves short of liquidity.47 The "stagflation" (a combination of high unemployment, inflation, and low growth) that emerged in the early 1970s provided a crucial experiment, and the verdict of informed public opinion went in favor of the monetarists. The sharp reduction in inflation achieved by the monetarist policy adopted in 1979 consolidated this victory.48 Although monetarist views are still far from universal among academic economists, the Federal Reserve became more and more monetarist during the 1970s; it adopted the growth targets for the money stock described earlier, and allowed most interest rates to be set by supply and demand. The resulting volatility further convinced the financial markets that the money stock was important, though this conviction is no longer universal. In any case, we must go more deeply into the process through which monetary policy operates. For this purpose we focus on Ml as already defined.49 Both currency and checkable deposits are subject to some control by the monetary authorities, but in practice they are mostly concerned with deposits, which account for most of M1. These deposits, of course, are liabilities of banks and are normally covered by bank assets (principally loans and other short-term investments). If the owner of a demand deposit wants to draw on it, whether by check or in cash, the bank


43

needs liquid assets with which to execute the transaction; most of its earning assets are too illiquid to be used for this purpose. These liquid assets are known as the bank's reserves and consist of its currency holdings (the so-called vault cash) and its demand deposits at a Federal Reserve bank. The reserves held by commercial banks against demand deposits and various other liabilities are the key to control of the money stock by the Federal Reserve System. Since neither form of reserves pays interest and their purchasing power is eroded by inflation, commercial banks will keep them as low as possible. The Fed can use this fact in two ways: It can change the reserves actually held by commercial banks, and it can alter the required ratio between a particular class of liabilities and the reserves held against that class. The first of these methods, known as open market policy, is used frequently, indeed almost continuously. To change the overall size of bank reserves, the Fed buys or sells financial instruments (particularly Treasury bills) to or from the banks. Thus if a bank buys T-bills from the Fed, it pays for them by drawing on its demand deposit at the Fed, thereby increasing its earning assets but reducing its reserves. Conversely, the Fed can increase bank reserves by buying Tbills from commercial banks.50 The second type of control over the money stock, by a change in reserve requirements, is exercised more rarely and usually signals a major change in monetary policy. Reserve requirements have to be handled gingerly because the Fed is also responsible for maintaining the commercial banks in sound financial condition; if the requirement is set too low, banks might be tempted to grant unduly risky loans. Whatever the method adopted, a change in reserves or reserve requirements induces the commercial banks to adjust their liabilities.51 Actually, banks adjust their liabilities mostly by adjusting their assets. When a bank provides a loan, for instance, it usually does so by giving the borrower a deposit against which he or she can write checks. The recipients of these checks will in turn deposit them in their bank accounts. In fact, monetary theory tells us that every loan creates a deposit. Thus, controlling the money stock is largely equivalent to controlling the volume of bank credit. 2.4.2 The Demand for Money

Having now analyzed the supply of money, we turn to the demand side. The willingness of individuals and business firms to hold assets in the form of money depends primarily on (1) the use they expect to make of it and (2) its opportunity cost.52 As to the use of money, a major component of money holdings is known as transaction balances, since they reflect the transactions that the holder expects to make in the near future. A wage-earner, for instance, receives wages once a week and uses them for consumption during the week. If consumption is spread evenly over the week, his or her money holdings will average one-half of weekly consumption. Similarly, many business firms receive and disburse money all the

44


time, but the inflow and outflow do not necessarily match in any short period of time, so money must be held to prevent a temporary suspension of operations for lack of cash. Again, the firm's transaction balance will be roughly proportional to the money value of the firm's transactions. In addition to their transaction balances, households and firms may hold money for emergencies, or to be prepared for such favorable opportunities as may present themselves. These precautionary balances, however, are inherently more flexible than transaction balances, and can be adjusted to the opportunity cost of holding money; if that cost is high, less money will be held. The reason is that, even in these days of "NOW accounts," money balances normally earn lower rates of return than other investments. When aggregated over all households and firms, the demand for money is written as a function of two variables: an indicator of the money value of transactions (usually nominal GDP) and an indicator of the relevant interest rate (usually a short-term rate such as the one for Treasury bills). The exact specification must also pay due attention to time lags since the adjustment of money holdings to these variables is not instantaneous. Now suppose that the central bank increases the money stock at a time when the private sector had already adjusted its money holdings to the prevailing interest rate. Some households and/or business firms will therefore find themselves with more money than they wish to hold at that rate. They will attempt to reduce their money holdings by exchanging money or bank deposits for financial investments, consumer goods, plant and equipment, and inventories. This attempt is bound to fail,because it merely transfers the excess money from one holder to another. The private sector as a whole cannot cut its total money holdings. As individuals bid for assets in an attempt to reduce their money balances, however, the prices of these assets are forced up, causing their yields as a percentage of the purchase price to fall. This process continues until the yields on nonmoney assets fall sufficiently to make it worthwhile to hold the enlarged money stock. Viewed in terms of the Flow of Funds framework, the process allows the Federal Reserve, by causing an expansion of the money supply, to provide an additional source of funds to the private sector. Total private sector sources thus exceeded total private sector uses, causing interest rates to decline. The establishment of a new equilibrium is aided by another factor: To the extent that increased liquidity leads to increased consumption and real capital formation, the demand for transaction balances will also rise, so the interest rate does not have to carry the full burden of adjustment. This is so regardless of whether the increases in consumption and capital formation result from higher quantities of higher prices. Just how much prices of different types of assets (and their yields) are affected depends on the degree of substitutability between them in individual portfolios. The prices and yields of assets that are poor substitutes for money will generally be less influenced by changes in the money supply than those of assets that are closely substitutable for money in terms of risk and liquidity. Thus the


45

yield on Treasury bills will be highly sensitive to changes in the money stock, while the price and yield on real estate, which is a poor substitute for money, will be influenced much less. Other assets, such as equities and long-term bonds, will be somewhere in between. Nevertheless, since virtually all assets are substitutable among each other to some extent, the impact of monetary policy is quite pervasive. It is hardly surprising, therefore, that participants in many different financial markets are alert to anticipated and announced charges in the rate of growth of the money stock. The Federal Reserve Board (or in other countries, the central bank) is aware of these repercussions as it influences the money stock via its open market operations, changes in the bank reserve ratio, and the discount rate, though it cannot be certain of the magnitudes involved. Money supply is also determined, in part, by the behavior of financial institutions (especially banks) through the process of credit creation. That process is not our primary focus here; the interested reader is directed to the excellent explanations in Goodhart (1975) or Mishkin (1995). 2.4.3 The Objectives of Monetary Policy

So far we have examined the effects of monetary policy; now we must ask what the central bank is trying to accomplish. In most countries the goal is steady, noninflationary growth of the economy with a high level of employment; the balance of payment may also be an important consideration. Within this general statement there is room for differences in emphasis, some countries being more averse to inflation or unemployment than others.53 In the United States and many other countries, moderate economic growth and a tolerable level of unemployment can probably be maintained (aside from occasional mild recessions) if real long-term interest rates and inflation are both kept below 5%. It would be even better if both were lower, but central banks have learned not to be too ambitious. Although monetary authorities, as we have seen, have considerable leverage over short-term interest rates, they cannot push them down too far without reviving inflation, which in due course will be reflected in higher nominal rates (see Section 2.3.3). Central bankers, in fact, must keep Fisher's equation constantly in mind; their power to set interest rates is much more limited than is commonly believed. For the same reason, central banks cannot reasonably aim to prevent all economic downturns. No doubt even a mild recession can cause considerable distress in terms of unemployment and bankruptcies, but it also serves to correct distortions created by the preceding boom.54 It is more important to prevent a recession from getting out of hand than to prevent it altogether. In practice this means allowing short-term interest rates to fall moderately when the economy shows signs of weakness but not to create excess liquidity that would sow the seed for subsequent inflation. The normal reduction of interest rates in a recession, incidentally, has another important consequence. Holders of bills and bonds welcome bad news

46


about the economy because lower interest rates raise the value of their investments. To some extent this seemingly perverse reaction also applies to the stock market, which (as explained in Chapter 6) tends to go up when interest rates go down. A partial offset to this effect, however, is the adverse impact of poor economic conditions on corporate earnings and dividends. In an open economy—and even the United States, with its huge domestic market, is now an open economy—the central bank will also be concerned about the balance of international payments, though it is not always clear how this concern translates into actual policy. Under the present regime of floating exchange rates, an external deficit need not lead to a more restrictive monetary policy, as was the case under the preceding system of fixed exchange rates; instead, the currency can simply be allowed to depreciate (or appreciate, in case of a surplus). Between 1980 and 1985, the U.S. dollar rose sharply, only to lose almost half its external value (by some calculations) in the 7 years since then; none of this had a detectable effect on Federal Reserve policy. In most other industrial countries, monetary policy also appears to be governed primarily by domestic considerations.55 2.4.4 Fiscal Policy and the Government Budget

Fiscal policy consists of those actions by the government that change the size and composition of public expenditures and the revenue from taxation. Many changes in expenditures or revenues, it should be noted, have nothing to do with fiscal policy thus defined; tax receipts, for example, will rise when the economy is booming even if tax rates remain the same. A change in tax rates does constitute an exercise in fiscal policy. The government surplus or deficit affects the securities markets through two main channels. The first follows from the fact that a surplus or deficit in the public sector normally alters the supply of government securities to the rest of the economy; it may also affect the size of the liquid assets held by the government. This condition is true whether or not the change in the budget balance results from fiscal policy actions. The second set of impacts arises because fiscal policy may alter the level of economic activity in the private sector, thus shifting the balance between sources and uses of funds within the economy as a whole. The use of fiscal policy to influence the economy was popular from the 1930s until the 1970s but has recently been deemphasized as attention shifts to monetary policy. The first channel just mentioned, however, is more important than ever because of the persistence of large federal deficits. As shown in Table 2.4, the government deficit is not entirely offset by private domestic savings and is in effect being financed by the Rest of the World. This does not mean that foreigners are buying all the Treasury bonds for which there is no domestic demand, although, in fact, considerable amounts of bonds have been sold abroad. On the whole, the Rest of the World has preferred to invest its dollar


47

earnings in other assets, such as corporate shares, foreign-owned factories, and real estate. It was shown earlier that government borrowing tends to raise interest rates unless it results in an increase in GDP large enough to create an offsetting demand for bonds. It is not yet clear what the effect of the large budget deficits in recent years has been. There may have been some favorable effect on GDP, but probably not enough to leave interest rates unaffected. On the contrary, the historically high level of real long-term interest rates during most of the 1980s and the early 1990s (well over 4% on Treasury bonds in 1995) suggests that federal deficits crowded out some domestic capital formation. We conclude with a brief discussion of the interaction between fiscal and monetary policy. It is brief because in most industrial countries (including the United States) this interaction is minimal. The Federal Reserve is under no obligation to assist the financing of the federal deficit by keeping interest rates low; we know by now that any attempt to do so would be self-defeating because of the resulting inflation. Since the Fed conducts its open-market operations mostly in Treasury bills,it may be said to give some indirect support through the large portfolio of T-bills it holds for that purpose, but this is of minor importance. The Fed does not normally deal in Treasury bonds at all, nor does it normally give credit to the federal government directly. Such direct credit, tantamount to financing the government deficit by printing money, is a major source of inflation in certain developing countries.

3 The Supply of Securities

As in the economic analysis of any market, our interest in the supply of securities stems first from its role, along with demand, in determining the market prices and, hence, the yields attached to various securities. In the case of asset markets, an assessment of the supplier is especially important because the value a buyer derives from an asset generally continues to depend on the supplier's performance even after the initial exchange has taken place. Take the purchase of a new automobile, for example. Even though you may own the car outright when you drive it from the showroom, the supplier's future performance can still be crucial to its value, particularly when you need spare parts or repairs under the guarantee. The purchase of a security (typically a bond or a corporate share) is an extreme case of this general characteristic of assets since the physical item exchanged has little or no intrinsic value. Apart from its potential as a decorative wall hanging, virtually all of its value depends on the supplier's future behavior. Financial claims vary, however, in the extent to which their value is ultimately exposed to poor supplier performance. A mortgage, for example, is relatively unexposed, given that the mortgagee is prevented from disposing of the underlying asset or markedly altering it without the prior consent of the mortgage holder.1 The value of common stock in a corporation, by contrast, is strongly affected by the actions of its managers and directors. This basic feature is shared by all securities to some degree. It should be clear from these examples what is meant by the "supplier" of a security. It is not the investor from whom it was purchased. His or her identity is usually unknown to the buyer as a result of trading through an impersonal market such as the New York Stock Exchange. Once a legal title to the security has been established the buyer needs to know nothing more about the previous owner, who is discharged from further responsibility (except in case of fraud or misrepresenta48

THE SUPPLY OF GOVERNMENT SECURITIES

49

tion). The more crucial actor is the ultimate supplier: the firm, individual, financial institution, or government agency against whom the security is issued. This ultimate supplier is called the issuer of the security. In this chapter we examine the supply of securities both in terms of the contractual characteristics of each main type and the way in which the actual performance of each is influenced by the behavior of issuers.

3.1 GENERAL CHARACTERISTICS OF SECURITIES

There are four key dimensions across which securities vary: 1. The dollar value of the anticipated return 2. The timing of these returns, including the time (if any) at which the principal is expected to be repaid 3. Their risk characteristics 4. Their negotiability Each of these may be influenced by the issuer's actions. The return on a corporate share, for example, varies with the profitability of the company. Profit will depend on the firm's new investment or product strategy decisions; it may also vary with general economic conditions, such as the growth of real GNP and the rate of inflation, that are beyond the firm's control. A company can alter the negotiability (also known as liquidity) of its securities by applying for a listing on a stock exchange, by having them delisted, or by arranging for them to be traded in some other competitive market. Issuers of securities also influence the volume of securities with particular characteristics supplied to the market in response to changes in price or other economic variables, in the same way as suppliers of goods and services do. Supply may be increased through new issues or reduced by retirement or repurchase. Similarly, the maturity of a corporate bond is altered when the firm chooses to exercise a call provision (discussed in Section 3.4.3) or goes into bankruptcy. In examining these processes our emphasis is on securities, defined in Chapter 1 as readily negotiable primary financial instruments. These are bonds issued by sizable corporations and governments, and corporate shares, but not the derivatives (options and futures) based on them. We also discuss, though more briefly, the supply of a number of other financial instruments, such as negotiable certificates of deposit issued by banks and mortgage-backed securities, as well as nontraded loans and deposits with financial institutions.

3.2 THE SUPPLY OF GOVERNMENT SECURITIES

Government agencies at all levels from federal to local are major issuers of securities to the financial markets. Indeed, their importance has continued to

50

THE SUPPLY OF SECURITIES

increase in the recent era of substantial deficit spending, the bulk of which is financed through issue of public debt.2 3.2.1 Federal Government Obligations

In the United States the largest single issuer of securities is the federal government. While its offerings encompass a range of different types of claims, they all share two basic features. First, because of the federal government's ultimate ability either to levy enough taxes or to print enough money to meet its obligations, its securities are regarded as being free of default risk. We shall therefore call them default-free. This designation does not mean, however, that U.S. government securities are "risk-free" in a broader and more meaningful sense of the term. An investor who purchases a long maturity bond with fixed coupon rate, for example, is exposed to the considerable risk that interest rates will rise, either leaving him or her locked into a low yielding asset or involving a capital loss if the bond were sold on the market; this price risk is common to all securities.3 There is also the very real possibility that the value of an investor's return on the bond will be eaten away by inflation so that the real rate of return is risky even though the nominal rate and principal are guaranteed. This exposure may be called inflation risk (see Section 3.2.4). The second feature shared by most U.S. government securities is ready negotiability. Of the total stock of federal government debt in the hands of the private sector, about 85% is in the form of marketable securities, which can be freely exchanged between the original purchaser and all subsequent holders. The markets in these securities are highly competitive.4 The only important exceptions are U.S. Savings Bonds and certain bonds issued to foreign governments. Given that the federal government is restricted to the issue of debt instruments, its securities differ primarily in their maturity characteristics. By offering a range of securities with different maturities, the government can obtain funds from different segments of the market.5 Four main classes of securities are offered by the federal government: Treasury bills, Treasury bonds, Treasury notes, and savings bonds. 1. Treasury bills are issued with maturities of 13 weeks (91 days), 26 weeks, or 1 year, generally in denominations of $10,000 and up.6 New "Tbills," as they are known in the markets, are offered to the public by auction, generally each Monday for 13- and 26-week bills, monthly in the case of notes, and quarterly for long-term bonds.7 Since they are "bearer" securities (i.e., possession of the instrument is accepted as proof of ownership), they are readily negotiable. 2. Treasury notes come next in the maturity spectrum of federal government securities. They are issued for a life of between 1 and 7 years. Unlike T-bills, notes carry an annual coupon rate, set so the notes are originally intended for sale at par (i.e., face value), which ranges from a minimum denomination of $1,000 upward.8 Notes are also actively traded. In the financial pages of any good newspaper,

THE SUPPLY OF GOVERNMENT SECURITIES

51

Treasury notes and other obligations are listed by maturity date and coupon rate, usually quoting a bid and ask price per $100 par value of bonds. This figure is customarily but confusingly reported in fractions of 1/32 of a dollar. The newspaper will also give the yield, which is the return (coupon plus the value of any discount) netted by buying at the current ask price and holding the note until maturity. 3. Treasury bonds are generally issued for the purpose of long-term financing at maturities between 7 and 30 years. Some bonds, however, are callable at the option of the Treasury (i.e., it can repay the principal at its discretion and stop paying interest) in the final 5 to 10 years prior to maturity. Otherwise, they differ from notes only in that they are issued for longer terms. 4. Savings bonds constitute the final major class of federal government securities. These are offered only to individuals and certain nonprofit organizations. Both "discount" and "coupon" series have been issued, but as we have already noted, these bonds are neither tradable in the market nor privately negotiable, and they are therefore not financial instruments as defined in Chapter 1. In the last few years the boundaries between the first three classes of Treasury securities have become less distinct as a result of the introduction of zerocoupon bonds, which, like T-bills, pay no interest and therefore trade at a discount prior to maturity. The owner of a large portfolio of ordinary long-term bonds can assemble the coupons from different bonds that are payable at the same date into a new security whose principal is payable at a certain date but that has no coupons. The principal of different bonds maturing on the same date can be similarly assembled. This operation, known as "stripping," was originally performed by private security firms who issued securities based on stripped Treasury bonds and notes, but zero-coupon bonds have also been issued occasionally by the Treasury itself. They have become widely popular, particularly among holders of Individual Retirement Accounts (IRAs) and Keogh accounts (basically IRAs for the self-employed), and Treasury securities are now regularly traded in stripped form. These "Treasury strips" mature on the fifteenth day of the second month of every quarter in the next 30 years.9 Since Treasury obligations (except for savings bonds) differ only in their maturity, the relation between yield and maturity is fairly clear-cut and important for many purposes. This relation is conventionally expressed in the yield curve, charted for three different time periods in Figure 3.1. Starting with the most recent data, we see that the yield was lowest for the shortest maturity shown (1 year) and rose steadily for the longer maturities. This relationship was also true in 1985, when the entire curve was at a higher level than in 1991. The pattern for 1985 and 1991 corresponds to a "normal" yield curve, such as is found most of the time. In 1980, by contrast, the yield curve was "inverted": The short maturities yielded more than the distant ones. The reasons for these diverse patterns are discussed in Chapter 4, where it will also be argued that the type of yield curve shown in Figure 3.1 is not very meaningful. In addition to the Treasury obligations listed above, there are bonds issued by federal agencies other than the Treasury; examples are the Federal National

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Figure 3.1 Yield curves for federal securities. Note: The yields are for "constant maturities," which means that they are interpolated from the quotations for actual notes and bonds of similar maturity. The yield for 20-year bonds is not given in the source and has also been interpolated. Source: Data from Federal Reserve Bulletin, September 1991 and earlier issues, table A23.

Mortgage Association and the Tennessee Valley Authority. Some of these are guaranteed by the Treasury, but even so they generally yield slightly more than similar Treasury bonds because agency issues are not as readily negotiable and because reliance on the Treasury guarantee may involve a delay. 3.2.2 Municipal Bonds

The other major source of government bonds are those issued by states, counties, cities and towns, school districts, and other special authorities such as sewer districts. They are collectively known as "municipals" in the United States. It is a long-standing federal policy that the interest earned on these securities shall be exempt from federal income tax.10 Municipals, which are also referred to as "tax-exempt" bonds, are therefore particularly attractive to individuals who face high marginal tax rates. For an individual in the 33% tax bracket, for instance, a 6% municipal bond produces as much after-tax interest as a 9% taxable bond. While granting this tax privilege, the federal government does not guarantee municipals against default. The individual authority must therefore back these bonds with its own revenue generating power. They must issue either General Obligation Bonds (G.O.'s), where an authority with theoretically unlimited taxing power pledges to collect the necessary revenue to meet its obligations on these bonds (a pledge called "full faith and credit"), or Revenue Bonds, which are entitled to access only the revenues of a specific project (such as a turnpike or a port).

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53

Because municipal bonds are not default-free, prudent investors want to know how secure each bond is. This information is provided by rating agencies, discussed more fully in connection with corporate bonds (see Section 3.3). Most municipal bonds enjoy high ratings, indicating a low risk of default. The exceptions arise in cases where the market or rating agency believe that an authority has an excessive quantity of debt compared with its realistic (rather than theoretical) revenue base. In fact, defaults have been rare since the Great Depression, although some have occurred.11 3.2.3 Bonds of Foreign Governments and International Organizations

Residents of one country may own bonds issued by the government of another country, but these are not default-free to their owners. Like the U.S. government, a foreign government can satisfy its domestic creditors, at least in nominal terms, by levying additional taxes or printing more money. This merely means that the government in question can always come up with the domestic currency. If the bonds are denominated in another currency (for instance, if Sweden issues bonds denominated in U.S. dollars), that is not enough to rule out default on externally held bonds since the debtor may not be able to obtain the foreign currency. Furthermore, the owner of foreign bonds that are denominated in some currency other than the owner's will have an exchange-rate risk (i.e., the currency in which the bond is denominated may be worth less in terms of the holder's own currency than when the bond was acquired). Nevertheless government bonds are often held by nonresidents; thus a sizable part of the U.S. government debt is now in the hands of private Japanese investors.12 Bonds issued by international organizations, such as the World Bank, are similar in their characteristics. The World Bank (officially known as the International Bank for Reconstruction and Development) has made it a practice to issue bonds in many different currencies. The risk of default on these bonds is not zero, but because of the close financial links between the bank and its shareholders (that is, the member countries), it is close to zero. 3.2.4 Index-Linked Bonds

As shown in Section 2.4.3, ordinary fixed-interest government securities are subject to inflation risk. This condition is the main reason for describing them as "default-free" rather than "risk-free." To achieve greater freedom from risk, such securities must offer protection against inflation, which can be accomplished by linking payments of interest and principal to a general price index such as the CPI. Thus a 3% index-linked bond with a face value of $1,000 would entitle the holder to an annual interest not of $30 but of $30 multiplied by the value of the CPI at the time the interest is due, and similarly for the principal. The interest rate of 3% would then be a real rate, not a nominal rate.

54


Although index-linked bonds have often been advocated, the U.S. Treasury has traditionally opposed them. In the official view, it appears, inflation is no more than a temporary problem, to be counteracted by appropriate monetary and fiscal policies instead of being accommodated. Figure 2.1 showed that inflation has persisted despite these pious intentions. Many other countries have adopted a more pragmatic attitude. In countries with high inflation, for instance in South America, government bonds without indexing are virtually nonexistent; the few that survive are literally not worth the paper they are printed on. Some countries with more moderate inflation have also responded to the demand for truly riskfree investments. One of these countries is the United Kingdom. According to the Financial Times, the leading British financial daily, the yield on index-linked bonds in mid-February 1991 was about 4%.13 The yield on comparable nonindexed bonds was around 10%, implying an expected inflation rate of about 6%. The actual inflation rate at that time was about 9%, so a considerable reduction of inflation was anticipated and has in fact occurred since then.

3.3 CORPORATE FINANCIAL POLICY

The activities of virtually all business enterprises require the firm to maintain a portfolio of assets. As described in Chapter 1, these may be in the form of physical plant, cash, and bank deposits required to facilitate transactions, or inventories and work in progress. In the case of smaller unincorporated enterprises and private companies, the funds required may come directly from the accumulated savings of owners, or perhaps from bank loans. As they grow, however, most firms sooner or later approach the securities markets for additional capital with which to finance their assets. The mix of securities supplied to the markets depends on the financial policy of firms. It is convenient to distinguish three key decision areas: 1. The optimal mix of debt versus equity 2. The desirable maturity structure of debt 3. The preferred source of debt funds (e.g., corporate bonds versus banks or finance companies) The ultimate objective is to minimize the total cost of funds required to finance any given level of assets. In a more general analysis, not attempted here, the assets themselves would also be treated as variables. Debt instruments have a simple but compelling attraction for the firm: They often are a cheaper source of funds than equity. This is the reality for two reasons. First, the interest expense on debt is deductible from the corporate income tax, whereas dividends on shares are not. Second, because debt holders have priority over shareholders in the allocation of the firm's earnings, and because they are promised a stable rate of return in the form of interest, the firm is


55

often able to raise debt at a lower expected return than it would have to offer on equity. Another consideration limits the usefulness of equity financing from the viewpoint of management. The shareholders are the ultimate owners of a corporation. They elect the board of directors, which in turn has the power to hire and fire executives. Most of the time the shareholders, especially if they are numerous and individually small, do not exercise their power; indeed many of them do not even bother to vote at the annual meeting required by law. In those circumstances, control of the corporation effectively resides in a small number of large shareholders, who are likely to be closely associated with management but who need not have a majority of the shares. Occasionally, however, the shareholders do matter, namely when there is danger of a corporate takeover (see Section 3.4.2). The management of a corporation often feels more secure if there are not too many shares in public hands. Bondholders do not vote (except if the firm goes bankrupt) and are therefore harmless as far as management is concerned. Why, then, do firms not finance themselves with 99.9% debt instead of the average of only 38%, which we shall soon observe in the aggregate data?14 The answer lies in the fact that the more debt a firm issues relative to its total assets, the more its long-run survival is put at risk.15 This answer follows from the constraint that if the firm fails to repay any part of the total interest or principal payment due on its debt during any year, all its debt immediately become repayable and debt holders have the right to force the firm into liquidation in order to recover their funds. Prospective holders of the firm's shares and bonds, as well as prospective lenders such as banks, recognize the increasing risk of bankruptcy as the ratio of debt to equity in a corporate balance sheet rises. A firm must therefore offer a higher rate of return on its securities the more debt it issues against its assets. Indeed, certain lenders may be unwilling to buy a firm's securities at any price if in their opinion the firm has too much debt already, or if its credit is not well established; this can be a serious problem for new firms. More expensive funds reduce the value of the firm. Up to a point, however, this effect is outweighed by the inherently lower cost of debt. The general relationship between the value of a firm and its debt-equity ratio is therefore of the form shown in Figure 3.2. Supplying more debt increases a firm's value so long as the chance of bankruptcy is relatively low. Within this context it should be noted that, given unchanged risk preferences, a more volatile economy (and hence more variable corporate profitability) will require firms to reduce their debt ratios, supplying more equity to the securities markets. The more volatile the corporate earnings, the greater the likelihood of inability to meet committed interest payments on any given level of debt. In practice, of course, bankruptcies will occur, so that we should look not only at the claim of each class of securities on the debtor's income but also at the rights attached to each type of security under liquidation. While some of the

54


Figure 3.2 Debt policy and a firm's market value

details may vary depending on the precise terms under which debt is issued, a typical ranking of liabilities is shown in Table 3.1. The liquidating agent's fees, accrued wages owed to employees, and unpaid taxes have the first claims on assets, ahead of other creditors. Holders of mortgages or other debt secured by a specific asset as collateral, however, have the right to liquidate that asset in order to recover their due. Next, creditors such as holders of corporate debentures, who are secured on the general assets of the firm, must be paid in full (assuming there are sufficient assets). Unsecured creditors, including trade creditors or holders of unsecured notes, then have first claim on what remains, followed by the holders of subordinated debt. The residual is then distributed pro rata to preferred and common stockholders.16 Table 3.2 lists the classifications used by the two leading bond rating agencies in the United States: Moody's Investors Service and Standard & Poor's.17 The table also shows the average yield for each rating class as of early 1991. Within the "investment" category the yields were not greatly different, but they rose steeply as the rating got worse. Returning to the firm's decision making process, once the optimal level of debt financing is determined, the company must decide what maturity structure is best suited to its purposes. This choice is influenced by two opposing forces. On the one hand—assuming the yield curve to be "normal" as defined in Section 3.2.1—short-term securities are generally a cheaper source of funds for the firm than those with longer maturities. Not only do they usually carry a lower interest rate, as shown by the yield curve, but also they offer greater flexibility in match-


57

Table 3.1 Ranking of Corporate Liabilities under Bankruptcy FIRST Liquidator's fees Accrued wages and employee benefits Taxes Mortgages and other debts secured on particular assets First ranking debentures Lower ranking debentures Unsecured notes Trade creditors Preferred shares Subordinated debt Common shares LAST The lower the ranking, the greater the probability that all or part of the original investment made in the security will be lost. In the case of corporate bonds, various rating agencies publish assessments of the risk of loss due to bankruptcy associated with particular bonds.

Table 3.2 Bond Rating Categories of Two Agencies and Corresponding Yields Category

Moody 's

Standard & Poor's

Yield"

Investment grades

Aaa Aa A

AAA AA A

8.7 8.8 9.4

Medium grades

Baa Ba B

BBB BB B

10.1 12.0 17.7

Speculative bonds

Caa Ca C

CCC CC C*

35.0C

—

D

[e]

Bonds in defaultd a

Average yield on Standard & Poor's rating. We are indebted to Kirk Ott for these estimates, which refer to February 1991. b

Payment of principal or interest in arrears.

c

Approximate average yield of bonds rated C, CC and CCC by Standard & Poor's.

d

Income bonds on which no interest is currently being paid.

e

Not meaningful.

58


Table 3.3 Aggregate Balance Sheets of U.S. Nonfinancial Corporate Business (trillions of dollars or percentagea at end of year) 1967

AT CURRENT COST Fixed assetsb Inventories Liquid assets Other assets TOTAL ASSETS

Bonds Bank loans Other liabilities TOTAL LIABILITIES NET WORTH MARKET

VALUEc

0.6 0.2 0.1 0.2 1.0

1987

1993

56 15 6 23

100

1.8 0.4 0.1 0.6 2.7

60 14 5 21 100

3.9 0.8 0.6 1.5 6.8 1.0 0.6 1.3 2.9

43

3.9

57

0.1 0.1 0.2 0.4

12

0.3

7 21 41

0.5 1.0

11 5 16 32

0.6

59

1.8

68

0.2

0.7

0.7

1.0 0.4 2.2 1.2

0.4 0.2 0.9 0.5 135

57

12

9 22 100 15

9 19

61

4.0 1.0 0.9 1.8 7.7

52 13 12 23 100

1.3 0.5 2.1

17

6 27

3.9

51

3.8

49

5.1

2.2 57

37

107

at % of net worth AT HISTORICAL COST Fixed assetsb Inventories Total assetsd Net worth Market value as % of net worth

1977

2.5 0.7 5.3 2.4

136 3.3 0.9 7.0 3.1

92

165

a

Percentage of total assets (at current cost) unless noted otherwise. Percentages were calculated from unrounded dollar amounts. b

Plant and equipment, residential structures and land.

c

Market value of corresponding equities; includes small amount for corporate farms, which are excluded from balance sheet data. d

Including financial assets.

Source: Federal Reserve Board, Balance Sheets of the U.S. Economy (Release C.9), September 20, 1994.

ing borrowings with the changing need for funds, so that the firm can avoid paying for unwanted capital when its financing needs decline. On the other hand, the use of short-term securities to finance illiquid assets requires the firm to "roll over" (refinance) its debt at frequent intervals regardless of the state of the capital markets. It is thus exposed to a risk of high interest rates and other unfavorable terms in periods of tight credit. These may also be periods when some supposedly liquid assets (particularly inventories and accounts receivable) turn out to be not so liquid after all. These considerations have led many companies to aim at achieving a match between the maturities of their assets and liabilities. Long-term funding (equities and bonds) is used to support fixed assets and working capital, which tend to grow along a fairly stable long-run trendline, though perhaps with some discrete


59

"jumps" when major new investments are made. The cyclical requirement for funds to finance fluctuations in inventories, accounts receivable, and cash requirements related to sales is met with short-term securities and bank credit. 3.3.1

Empirical Evidence

An indication of where firms end up in the pursuit of their financial objectives is given by the average balance sheet structure of U.S. nonfinancial corporations, as derived from the Federal Reserve's aggregate data and reported for selected years in Table 3.3. The table is divided in two parts. In the top part tangible assets are valued at "current cost" (essentially equal to replacement cost), which is most meaningful from the economic point of view; as shown in Chapter 1, replacement cost is what interests anyone considering the takeover of a corporation. In the lower part, assets are valued at "historical cost" (i.e., at what they cost when they were originally acquired, less depreciation), emphasized by conventional accounting practices. For financial assets and liabilities the distinction between current and historical cost is generally of little significance. Considering first the current cost data, we see that in 1993 net worth, also known as shareholders' equity, was about 49% of total assets, significantly less than in the earlier years shown. In general, the equity originates from net sales of shares, from retained earnings, and from increases in the nominal value of fixed assets due mostly to inflation. The liabilities consisted largely of bonds, trade debt, bank loans, and mortgages.18 The top part of Table 3.3 shows that in the late 1970s shareholders' equity financed an unusually high percentage of corporations' total assets. By 1987 the ratio of net worth to total assets had returned to the ratio prevailing in 1967 (and also, by and large, in earlier years). One may perhaps infer that corporations had thus corrected a temporary imbalance in the structure of their liabilities. As is shown in Section 3.4.1, they did so mostly by repurchasing their own shares, thereby taking advantage of the low ratio of the market value of these shares to their theoretical value implicit in the balance sheet.19 The stock market, according to this argument, had grossly undervalued the equities of nonfinancial corporations in the late 1970s and early 1980s; this undervaluation had not been fully eliminated by the end of 1987, when the market value was still only 57% of net worth. By the end of 1993 the market value exceeded net worth at current cost by a considerable margin (see also Figure 3.3). Remember, however, that the aggregate balance sheet at current cost reflects a number of debatable assumptions made by the statisticians at the Federal Reserve and the U.S. Department of Commerce. The omission of intangible assets (patents, goodwill, etc.) is a serious limitation of the published balance sheets. The historical cost data in the bottom half of Table 3.3 present a rather different picture. The figures for fixed assets, in particular, are much lower than their counterparts at current cost. As a result, net worth is significantly lower at historical cost than at current cost. Instead of the undervaluation of equities

60


Figure 3.3 Market valuation and indebtedness of U.S. nonfinancial corporations. Note: Data from Federal Reserve Board, Balance Sheets of the U.S. Economy (Release C.9), September 20, 1994.

pointed out in the preceding paragraph, there now appears a marked overvaluation in 1967 and 1993, though not in 1977 and 1987. Which of these contrasting interpretations should we believe? The current-cost calculation has the backing of economic theory, but that does not imply it is believed by the market. If the current-cost approach is correct, the market value of equities should have moved closer to the underlying net worth, as indeed it had done with a vengeance by 1993. Needless to say, one such observation is not conclusive, and the problem is discussed further in Chapter 6. It is also of interest that net worth is a much smaller fraction of total assets in the private financial sector of the economy than in the nonfinancial sector. According to the same source as was used for Table 3.3, the total assets of private financial institutions at the end of 1991 were $13 trillion and their net worth was only $1 trillion. Moreover, the ratio of net worth to total assets has tended to shrink in recent years, again in contrast to the other sector. The Flow of Funds Accounts provide a very detailed breakdown, both of sectors and of transactions. An example that provides some perspective on recent developments in the financial markets is the "Sector Statement of Saving and Investment" for nonfinancial corporate business, shown (again in condensed form) for some recent years as Table 3.4. We see that in 1980 and 1993 corporations issued a relatively small amount of equities but in the other years they bought back their own equities on a large scale. In fact, corporations were net purchasers of their own equities from the latter part of 1983 through the first quarter of 1991, a phenomenon to which we

THE SUPPLY OF CORPORATE SECURITIES

Table 3.4

Saving and Investment of Nonflnancial Corporate Businessa (billions of dollars)

Profits before tax — Tax accruals --Dividends* = Earnings retained in U.S. + Foreign earningsc + Depreciation charges + Valuation adjustmentsd = GROSS SAVING

Net change in financial assets --Net equities issued --Netborrowinge = NET FINANCIAL INVESTMENT

+ Real investment = GROSS INVESTMENT Sector discrepancy a

61

1980

1985

1990

1993

1994

181 67 45 69 19 173 -61 200

166

70 74 22 20 256 44 352

231 93 117 21 43 327 22 412

293 117 159 18

356 142 158

358

36 462

379 33 502

83 -85 198

86 -63 167

83 22 73

127 -41 119

-31

97 10 121

51

55 35

--39

--12

--33

256 222

375 344

403 365

440 428

522 489

- 23

8

47

34

13

—34

Excluding farm corporations.

b

Less earnings received from abroad.

c

Earnings retained abroad.

d

The Inventory Valuation Adjustment changes inventories from historical to current cost; the Capital Consumption Adjustment does the same for depreciation charges.

e

Including foreign direct investment in the United States.

Source: Federal Reserve, Flow of Funds Accounts (Release Z.1), March 8, 1995, and earlier issues.

return in Section 3.4.1. As a result, they had to borrow heavily, because they also had to finance real investment and were acquiring other financial assets on a large scale. When repurchases of shares came to a temporary end in the early 1990s, borrowing declined sharply. This is the most striking development revealed, but the attentive reader will notice much else of interest, including the increasing tendency of these corporations to keep their earnings abroad (presumably because the dollar tended to fall from 1985 on).20

3.4 THE SUPPLY OF CORPORATE SECURITIES

The preceding theoretical discussion suggests that a cost-benefit calculation for different types of securities, in conjunction with the firm's funding requirements and the risk of bankruptcy, leads most companies of significant size to issue a range of securities. These include: • Common stock, which has last claim on earnings and assets but stands to benefit from higher profits in successful years and to bear the risk of lower or negative profits in unsuccessful years. The common stockholders are

62


the owners of the corporations and elect the board of directors at the annual meeting. In the United States, corporations generally have only one class of common stock, but in other countries they may have more than one class with different claims to dividends or different voting rights. • Preferred shares, which claim a predetermined dividend ahead of common stockholders if sufficient earnings are available after payment of interest, but no more than their fixed dividend in successful years. They may be either cumulative preferred, in which case unpaid claims on past dividends will cumulate until funds are available, or noncumulative, in which case shortfalls are not carried forward to better years. Since the noncumulative variety is open to abuse—a firm may conceivably juggle its reported earnings so as to show an insufficient amount for preferred dividends—most preferred shares issued in recent years are cumulative. • Various forms of fixed-interest corporate debt with first claim on earnings and in most cases an enhanced ranking under bankruptcy. These include first and second ranking debentures, unsecured notes, and subordinated debt, with a wide range of maturities (usually varying between 5 and 20 years) designed to match the pattern of funding requirements over time. In addition, large corporations sometimes issue commercial paper (also known as "open market paper"), short-term IOUs that are sold directly to investors. Except for being subject to default risk, commercial paper is similar to Treasury bills. The interest rate on such paper is higher than the T-bill rate but lower than the prime rate charged by banks on loans to their best customers. • Mortgages and other liabilities with claims on a specific asset, such as the firm's land and buildings or a particular piece of equipment, again usually with fixed interest payments. These are augmented by short-term borrowing from banks or other financial institutions, and indirect financing by means of leasing arrangements. 3.4.1 Corporate Equities

As with its products, a firm may alter the volume of securities it is supplying to the market at any time. In the case of equities this change may be accomplished in four main ways: through flotation of new shares, rights issues, stock splits (and the related methods of bonus issues or stock dividends), or share repurchase. When a corporation is initially established, its charter specifies the number of shares it is authorized to issue, generally at a stated par value.21 These shares only acquire economic significance, however, when they are actually issued. Stock may be issued privately to individuals connected with the company or its officers, or by public offering. In the latter case the shares must be registered with the Securities and Exchange Commission (SEC) and a prospectus must be made available (see Chapter 11). The prospectus must disclose at least the legal


63

minimum of information about the corporation's current and proposed activities, its existing assets and liabilities, its directors and their beneficial interests, and so on. Provided it has sufficient authorized capital and is not under any legal injunction, a corporation may issue shares at any time.22 However, the statutory requirements (and, in the case of listed shares, the rules of the stock exchanges) mean that the transactions costs involved are usually significant. Since a high proportion of those costs is independent of the size of the issue, most companies issue new shares infrequently and in large parcels.23 Once newly issued shares have been subscribed and the funds collected from investors, they become permanent capital. As the corporation continues in business and retains part of its earnings, its share price will typically rise above the original par value at which the shares were initially bought by the founders. Any issue of new shares will therefore be made at a price that includes a premium over the par value, reflecting the greater worth of a share in the established company. This premium rewards the initial stockholders for their successful initiative. Most public issues are underwritten by investment bankers24 who, for a percentage of the final value, guarantee that the corporation will receive an agreed amount from the issue. If some of the offered securities remain unsold after a specified period, the underwriters are forced to absorb them temporarily into their own portfolios to make up the cash shortfall; the market price is then likely to fall below the issue price. Less frequently, the issue will not be underwritten, but the investment banker will operate on a "best efforts" basis for a lower fee. Certain investment bankers, the "venture capitalists," specialize in the shares of newly established firms, which they may keep in their portfolio until the conditions for a public offering appear favorable. Instead of offering its shares to all comers, a firm may choose to sell new equity to its existing shareholders by means of a rights issue. In this case, each existing shareholder receives the right to purchase a number of new shares in proportion to his or her current holding. Thus a "1 for 4" rights issue would allow a shareholder to purchase one additional share for every four currently held. Since companies wish to ensure that a new issue is successfully subscribed, the new shares are offered at a price below the current market value, indeed below the price expected to prevail after the shares have been "diluted" by the new issue.25 If the issuing firm has judged the market correctly, the "rights" will therefore have a money value and they will be traded as a separate security until they expire. An investor who exercises the rights in full will maintain the same proportion of voting shares as before the issue. Alternatively, an investor who does not wish to subscribe can sell the rights in the market as a compensation for the fall in the stock's price resulting from dilution. Depending on how well the issue is received (i.e., on whether it attracts many new buyers) he or she may also realize a capital gain or loss.

64


Corporations can also alter the number of their shares outstanding by stock dividends, also described more appealingly as "bonus issues." When the generous corporation of which you are a shareholder "pays" a stock dividend (say, one new share for every twenty currently held), it may be premature to break out the champagne. Because the firm's net worth and earnings potential are unaffected, it may be argued that the same total value is now divided among more units of stock so that each is worth less—another example of dilution. Nevertheless, many respectable corporations do declare regular or occasional stock dividends. In doing so they usually leave the cash dividend per share unchanged; consequently each shareholder collects a larger payout. If so, champagne may be in order after all. In many cases, declaring a stock dividend is merely an indirect way of increasing the cash dividend. It is convenient and customary to keep cash dividends at a round figure (such as 60 cents) per share, and stock dividends introduce flexibility without going into odd figures. By adopting a stated policy of periodic (say, annual) stock dividends, a corporation in effect promises its shareholders a steady rise in cash dividends. Another frequently used way of increasing the number of shares is through a stock split. Thus if shares are split 2 for 1, each shareholder receives two new shares for one existing share held. Less common is a reverse split (1 for 2, for instance), which reduces the number of shares outstanding. One motive for declaring a stock split is to increase the demand for shares by adjusting the price per share downward into a more desirable trading range. Shares are normally traded in "round lots" of 100; transaction costs per share are larger for "odd lots" of smaller size. If the price per share is high, the round lot may be too expensive for small investors, and trading may lack liquidity. A reverse split, by contrast, may be undertaken to remove the unfavorable image often associated with low-value shares, which in extreme cases are called "penny stocks." Some executives also argue that stock splits (and to a lesser extent stock dividends) send a positive signal to investors about the firm's prospective growth, thereby increasing the total market value of the firm. Several researchers have examined the effects of actual splits. The basic method, known as an "event study," is to estimate the "normal" path of a stock's price on the assumption that, except for the split, the price would have maintained its historic relation to a general index of share prices. This path is then compared with the actual movement in prices around the time the split takes place. An influential paper by Fama and others (1969) using this approach failed to find any significant change in the market value of the firm following a split or stock dividend. Over the period immediately prior to a split, however, stocks on average gave an abnormally high return. The probable explanation is that management tended to split the stock only after it had risen strongly. More recent studies have reached similar conclusions. On the question of liquidity, Copeland (1979) found that after a split transactions costs tended, if anything, to increase as a percentage of value, and that the turnover of the shares (the volume traded divided by the number of outstanding shares) often fell following a split.


65

The final method a corporation may use to alter the supply of its securities is to repurchase them. As shown in Table 3.5, nonfinancial corporations have on balance repurchased their shares on a large scale in recent years. Share repurchase may be undertaken either by the corporation buying its own shares in the open market or by a tender offer in which it offers a stated price for all shares tendered to it prior to a closing date or until its desired quota is reached. Companies that have accumulated cash and lack promising investment opportunities within the firm may decide to repurchase some of their shares as a way of giving investors a return in the form of capital gains rather than dividends. Alternatively, the management may regard its shares as currently underpriced and signals this to the market by offering to purchase them for cash, in the hope that the market will react by increasing the price. Yet another motive, discussed more fully in Section 3.4.2, is fear on the part of management that the corporation will be taken over by unfriendly investors, who may replace the incumbent managers and directors with their own appointees.26 In any of these cases the repurchase results in a decline in the total assets held by the firm and a reduction in the supply of its shares to the market; unless the company has surplus cash, it will also lead to an increase in debt. Table 3.5

Net Issues and Purchases of Corporate Equities (billions of dollars)

1985

1990

1993

1994

10.4 2.1 2.4 14.9

-84.5 15.8 3.7 -65.0

-63.0 10.0 7.4 -45.6

21.3 38.2 60.6 120.1

-40.9 28.6 43.9 31.6

--12.3 24.8 -1.8 4.2 14.9

-124.0 44.3 10.3 4.4 -65.0

-21.2 -22.8 14.4 -16.0 -45.6

-83.7 65.6 128.8 20.5 120.1

--109.4 17.4 122.7

3.5 1.7

88.7 81.9

65.3 47.4

316.8 231.8

128.5 91.7

1980 a

ISSUING SECTORS

Nonfinancial Financial* Foreign TOTAL PURCHASING SECTORSc

Householdsd Financial* Mutual fundse Foreign TOTAL

0.9

31.6

OPEN-END MUTUAL FUNDS

Shares issued Purchased by householdsd a

Excluding open-end mutual funds.

b

Banks, insurance companies, real estate investment trusts, brokers and dealers, and closed-end funds; does not include open-end mutual funds. c

Excluding purchases of mutual fund shares.

d

Including bank personal trusts after 1980.

e

Net purchases by open-end mutual funds of primary equity issues (see text).

Source: Federal Reserve, release Z.1, March 8, 1995, and earlier issues.

66


The Flow of Funds accounts include statements showing the net supply and demand for specific types of financial instruments. Comparison of these statements over time indicates not only variations in the size of net issues of each class of financial instrument (i.e., the net amount of new securities coming onto the market in a year) but also changes in the identity of the purchasers. Table 3.5 makes such a comparison for corporate equities for selected years from 1980 through 1994. The three parts of this table reflect a distinction between primary and secondary equities. Primary equities are issued by firms as an incidental part of their main business, which may be manufacturing, banking, retailing, or whatever; secondary equities, by contrast, are issued by mutual funds, whose main business is precisely the selling of their own shares. As is explained more fully in Section 3.5, the principal assets of a mutual fund are the primary securities (stocks and bonds) of other companies, against which they issue their own shares. The distinction between primary and secondary equities is necessary to avoid double counting. As noted in Section 3.3.1, net equity issues can be negative, as they were in most of the 1980s and 1990s, particularly for nonfinancial corporations. The household sector has been a net seller of primary equities in every year since 1961, though in many years these net sales have been wholly or partly offset by net purchases of mutual fund shares. The financial sector (excluding mutual funds), on the other hand, has usually been a net buyer of equities; so, except in a few years, has been the rest of the world. During the stock market boom that crested in August 1987, therefore, the public was taking profits while the financial sector and the rest of the world continued to buy. This behavior casts doubt on the belief, widespread among financial "experts," that the public is usually wrong and the experts usually right. The massive net repurchases of equities in recent years, incidentally, shed new light on the role of the stock market in the economy. It used to be thought that its main economic function is to aid in the financing of investment by creating a liquid market in which new share issues can be readily absorbed. Recently, however, nonfinancial corporations have on balance used the stock market not to sell their own shares but to buy them back. Admittedly this may be a temporary phenomenon, but it helps to explain why the spectacular crash of 1987—at least as severe as the notorious crash of 1929—had so little impact on the economy as a whole. Repurchases by corporations aside, households have in effect been selling primary equities to the financial sector (which in this context essentially means pension funds, life insurance companies, and mutual funds) for many years. As shown in Table 3.4, a large part of household saving takes the form of acquiring claims on these same institutional investors. One possible interpretation of this interchange is that households have gained more confidence in the management of equity investments by professional investors as compared to their own. Another interpretation—not necessarily inconsistent with the previous one—is that


67

there are significant economies of scale in investment management, so that institutions can do it more cheaply than individuals. 3.4.2 Corporate Takeovers

Reference was just made to management's fear of a hostile takeover. Attempts to gain control of a company by buying a sufficient number of shares are nothing new, but they appear to have become more common and are often dramatic enough to make headlines in the newspapers, especially when they involve many billions of dollars. The incumbent executives typically denounce the would-be "raiders" to the shareholders in terms of righteous indignation, accusing them of financial irresponsibility, intentions to "loot" the company by selling off assets, "sheer greed," and other violations of business ethics. The shareholders generally adopt a more relaxed attitude as they watch share prices soar during the battle for corporate control. A variety of tactics can be employed by the incumbents in the course of this battle. Not infrequently they take the raiders to court for alleged infractions of the securities or antitrust laws. They may also prevail on state legislatures to enact "anti-takeover" legislation.27 Another approach is to find a "white knight," a friendly third party willing to give financial support to the incumbents. If these tactics appear likely to succeed, the raiders can sometimes be persuaded to sell their accumulated shares to the incumbents at a profit, a practice known as "greenmail." The attacking side has fewer options; its main tactic is to raise the price at which they will buy shares. The disinterested observer of these striking episodes should remember, first of all, that a corporation belongs to its shareholders, not to management. Those who attempt to gain control of a company must bid more than the prevailing market price, and they would not do so unless they consider its shares to be undervalued. This assessment usually means that they expect to obtain a higher return from the company's assets than the existing management, either by using these assets more profitably or by selling them to other firms. Takeovers, therefore, may lead to greater efficiency, and that is the main argument against making them too difficult by legislation or otherwise.28 Several studies in the finance literature on the actual effects of takeovers (most recently by Roll, 1986) suggest that existing shareholders nearly always gain, but that the raiders on average do no better than break even; in other words, the latter tend to pay a fair price. This evidence supports the theoretical notion that takeovers promote efficiency. 3.4.3 Corporate Bonds

We turn now to corporate actions that influence the market supply of bonds. New bonds are generally issued against a trust indenture or trust deed, a legal agreement in which the corporation promises an independent trustee to comply

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with provisions regarding the payment of interest, disposal of assets, issue of additional bonds, and notification of changes in the firm's financial position. The trustee represents the bondholders when there is a default. Bonds may be issued in two ways that are about equally important. In a private placement, a broker or investment banker seeks out one or more buyers for the new issue and arranges a direct trade between issuer and investor. A public offering is usually underwritten in the way previously described for shares. The supply of corporate bonds may be reduced either by repayment on maturity, by repurchase in the open market, or by redeeming them prior to that time under a call provision in the bond indenture. Not all bonds are callable, but in the many cases where a call provision exists, it enables the firm to replace debt issued during periods of high interest rates with cheaper sources of funds when rates become more favorable. A call provision is an example of an option (see Chapter 8). Clearly, call provisions reduce investors' opportunities for capital gains on high-yielding bonds when interest rates decline. In order to sell callable bonds, therefore, the issuer must offer some mix of higher yield and call protection. The latter may take the form of a promise in the indenture that the bonds will not be called before a certain time, or the specification of a penalty to be paid over the face value if the bond is called. 3.4.4

Junk Bonds

Until the early 1980s underwriters would not normally support a public bond offering unless the bonds were of investment grade (see Table 3.2), implying a low risk of default. If a bond had a low grade that was the result of unfavorable developments subsequent to the original issue, the bonds were known as "fallen angels." A study by Hickman (1958) suggested that such bonds tended to be undervalued by the market; in other words, that too much weight was given to the risk of default.29 When the implications of this study were belatedly realized on Wall Street it became more common to make initial offerings of bonds with a lower grade and, needless to say, a higher yield. These are usually called "junk bonds," though the underwriters prefer the more appetizing term "high-yield bonds." Such bonds may also have a lower priority than other bonds in case of liquidation, though they would still rank ahead of common stock. The emergence of junk bonds has enlarged the financing menu for corporations, already discussed at the beginning of Section 3.4. As a source of funds they probably compete mostly with new equity issues, which managers often considered undesirable because they endanger corporate control and because dividends, unlike interest, are not tax-deductible to the paying corporation. At first, most junk bonds were issued to facilitate corporate takeovers (see Section 3.4.2), but the financial advantages of issuing junk bonds have been increasingly understood by well-entrenched managements as well. It appears that the changing


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balance between new shares issued and shares repurchased (noted at several points in this chapter) may be due, at least in part, to the new financing opportunities afforded by junk bonds. In assessing the performance of junk bonds as a financial instrument it should be borne in mind that they became popular when general economic conditions were unusually favorable. The previous recession bottomed out in late 1982; until 1990 the economy saw fairly steady growth; inflation was kept under control; corporate profits were rising. A severe test for junk bonds was provided by the most recent recession, which ended in 1992. A sharp fall in corporate profits could have caused widespread defaults on junk bonds and discredited the entire concept.30 Corporate profits did fall somewhat and there were a number of defaults, but they were not on a massive scale. Although it is still too early for a definitive verdict on junk bonds, the evidence to date suggests that on the whole they weathered the recession of 1990-1991 fairly well. In fact, several new issues of junk bonds in 1992 and 1993 were well received by the market. A default, incidentally, does not necessarily mean that all is lost. Even though a company runs out of cash, it may still have assets that can be sold to pay something—sometimes all it owes—to bondholders. It is not yet known whether the total return on the junk bonds issued during the 1980s (including the high interest paid initially and the subsequent losses on defaulted issues) was high enough to reward investors for the obvious risks they knowingly undertook in buying these low-rated securities, but there is little doubt that most holders of junk bonds came out well despite some anxious moments. 3.4.5 Convertible Securities

Various "hybrid" securities are also issued by the corporate sector, the most important of these being convertible securities. In the case of convertible bonds, the company issues a standard long-term bond at a fixed coupon rate, attached to which is an option31 permitting the holder to exchange each bond for a specific number of shares of common stock. In some instances, the bond may,only be converted during a specific period; for example, not prior to 2 years following the original issue of the bond, nor after 10 years have elapsed. Alternatively, the "conversion ratio," that is, the number of shares per $1,000 of bonds redeemed, may decrease after some point to encourage early conversion, or the agreement may include a call provision which allows the company to force conversion after a certain date. Convertible bonds therefore usually amount to a delayed issue of equity. As such, they may offer several advantages to the company. The first flows from the fact that the option to convert is worth something to the investor because if the share price rises sufficiently, there will be a profit to be made in the exchange. A conversion ratio set at 20 shares per $1,000 of bonds, for instance, effectively gives the holder the right to buy shares from the company at a prices of $50 per share. If 3 years hence the share is trading at $60, the investor makes

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a handsome return in addition to the value of the coupon payments on the bond during the interim. It is precisely because this option is valuable that the investor will be prepared to accept a somewhat lower coupon rate on the original bond. By issuing convertibles, therefore, a company can cut its cost of financing in the short run.32 A possible further advantage to the issuing corporation (or at least to its management) is that existing control is not diluted in the short run. A group of major shareholders can thus effectively increase the equity base of the firm without the immediate threat to their voting control that a substantial new equity issue might entail. In addition to convertible bonds, convertible preferred shares with analogous provisions are also issued by some firms. In that case, preferred shares may be exchanged for common shares at a price specified in advance.33 3.4.6 Partnership Units and Business Taxation

In recent years a new type of corporate security has been introduced that does not fit into any of the above categories. Before we describe it, an overview of the tax treatment of business firms will be helpful.34 We saw in Chapter 2 that there are two main classes of firms: corporations and unincorporated enterprises. The latter class can be divided further into sole proprietorships and partnerships. Sole proprietorships are firms with a single owner who receives all the profits, bears all the losses, and is personally liable for the firm's debts. The owner pays income tax on the profits and may take a deduction (subject to certain limitations) for the losses. There are no other federal taxes on such firms, which are typically small. Partnerships are basically similar in their tax status to sole proprietorships. The main difference is that there is more than one owner. Profits and losses are divided among the owners according to a formula agreed upon when the partnership was set up. In the simplest type of partnership, however, each partner is personally liable for all the firm's debts. The partners pay income tax on their share of the profits and may be able to deduct their share of the losses. The partnership as such is not subject to federal tax. In a more complicated form of partnership there are two classes of partners, general and limited. The division of profits and losses is again determined by the initial agreement, but here only the general partners are fully liable for the firm's debts; the limited partners cannot lose more than their investment. The general partner or partners—there may be one or more—usually manage the firm. The tax treatment is again similar to that of sole proprietorships. Turning now to corporations there are again two subspecies. Small corporations, as defined by the Internal Revenue Code, are essentially treated as partnerships; that is to say, the corporation as such is not taxed but the shareholders pay income tax on any dividends they receive. Such corporations are also known as "Subchapter S" corporations after the part of the tax code that deals with them. The larger corporations that do not qualify for Subchapter S are of princi-

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pal interest in a book on financial markets. Those whose shares are traded on exchanges or over the counter belong to this second subspecies. Unlike all the firms discussed so far, they are taxed directly through the corporate income tax. In addition, the shareholders pay the individual income tax on any dividends they receive, but there is no deduction for any losses reported by the corporation. Consequently, corporate profits are subject to double taxation: once at the corporate level and again (assuming dividends are paid) at the individual level.35 Evidently large corporations have a strong incentive to avoid this double taxation, since doing so would make their equities more attractive. In the 1980s a legal way of avoiding double taxation was found. A few listed corporations— we have identified only about a dozen—organized partnerships to hold a portion of their common stock.36 The general partner is the corporation itself, and the limited partners are the holders of "partnerships units," who take the place of the common stockholders. These units trade just like ordinary equities. The corporation still pays the corporate tax on its share (as the general partner) of the profits, but the limited partners pay only the individual income tax on the dividends they collect. The dividend yield on the currently listed partnership units is generally much higher than the typical yield on common shares issued by otherwise similar corporations. Indeed, it is close to the typical return on junk bonds—between 9 and 11% in early 1995. The history of these units is too short to determine if the risk is also comparable to the risk on junk bonds. However, the interest rate on bonds is fixed, whereas the dividends on partnership units may rise or fall over time. The merits of these units as an investment, and as a source of funds for the issuers, need further investigation. As mentioned already, the number of firms with listed partnership units is small. From 1987 on, new partnership arrangements have not been permitted, and the existing ones will lose their tax exemption in 1997, at which time they will presumably disappear. The main reason for discussing them is the opportunity to deal briefly with an example of the way business taxation can impact the supply of securities.

3.5 MUTUAL FUND SHARES

Mutual funds are not ultimate suppliers of securities in quite the same way as corporations or governments. They pool existing securities and then issue their own shares against this portfolio. In this fashion they generate securities with risk-return characteristics that individuals may be unable to reproduce; more specifically, they provide diversification. Because of high transactions costs and lack of information, there are limits on the diversification that an individual investor, particularly if her portfolio is small, can achieve. An annual management fee and often also an initial sales fee are charged for this service.37 In the past, mutual funds invested mostly in equities, but in recent years

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funds specializing in bonds (federal, municipal, or corporate) have become prominent. In the United States there are now thousands of mutual funds, on which data are published every day in the financial press. All of them can be divided into two main categories depending on their supply characteristics: openend funds and closed-end funds. The most numerous funds are in the open-end category.38 Here the management stands ready to redeem an investor's share on demand at a price (known as Net Asset Value, or NAV) equal to the market value of the underlying assets. The management is also empowered to issue new shares at any time at the NAV in the case of so-called no-load funds. New shares are issued at a premium to cover marketing costs in the case of "load" funds.39 This premium or sales charge is typically 8.5%, so the buyer has an immediate loss if she changes her mind. Consequently load funds are not suitable for in-and-out traders. By buying and selling the underlying securities, the fund manager keeps assets in balance with the outstanding shares. At the end of 1991, open-end mutual funds had total financial assets of $478b, of which 39% was invested in equities and most of the remainder in government and corporate bonds. In a closed-end fund, the management has no obligation to redeem an investor's shares or to sell additional shares to the public. At any time, the fund has a portfolio of securities against which it has issued a fixed number of shares. Most closed-end funds may, however, make new issues or repurchases of their own shares to and from the market at the manager's discretion. Such funds, which unlike open-end funds are listed on a stock exchange or over the counter, are usually quoted at a discount to Net Asset Value. It does not follow, as is sometimes maintained, that this feature makes them a good buy; the discount merely reflects the management fee, which is deducted from the payments to shareholders. When a closed-end fund is organized, its shares are typically offered at NAV, but in most cases these shares develop a discount sooner or later. Buying a closed-end fund at its initial public offering is evidently a risky proposition. Closed-end funds generally pay out earnings from dividends and interest, along with net realized capital gains, to shareholders.40 In open-end funds, the accrued earnings and capital gains are usually credited to shareholders in the form of additional shares in the fund. As mentioned earlier, the principal service provided by mutual funds is diversification. That, however, is not how they present themselves to the investing public. There is often an explicit or implicit claim that the fund's management has special skill in selecting good investments. Several studies testing this claim have been conducted, and their results are overwhelmingly negative.41 Despite their reliance on sophisticated analysis, many funds perform no better than the stock market averages. In any finite period of time, of course, some funds do better than others, and there are always a few that improve on the averages, but their performance appears to be due more to luck than to skill. This disconcerting observation has led to the creation of index funds, whose

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portfolio is composed in approximately the same proportions as a market average such as the Standard & Poor 500.42 These funds have no need for highly paid analysts, so their expenses are modest. Their performance is necessarily close to the chosen average. Although index funds have grown in importance, most mutual funds still pursue the will-o'-the-wisp of above-average performance. Mutual funds (particularly the open-end variety) can also be categorized by their stated investment objectives. Income funds, as the name implies, promise their shareholders relatively large dividends, while growth funds aim at capital gains. Index funds, of course, are somewhere between these two extremes. Socalled value funds try to select companies that are undervalued by the market. Large fund managers usually operate a family of funds that cover the spectrum from income to growth. There are also funds that specialize in particular industries or particular countries. The latter are known as country funds and (if they are of the closedend type) may have large premiums over Net Asset Value when the country in question makes it difficult for individual foreign investors to buy equities on their own. Country funds have proliferated for two reasons: More and more countries are relying on private corporations to stimulate their economic development, and investors have become increasingly interested in diversifying their investments internationally rather than in just one country. One of the minor difficulties in understanding the financial markets is that the same word is sometimes used with more than one meaning; the meaning has to be inferred from the context in which it is used. Mutual funds provide an example. The management of an open-end fund will occasionally decide to "close" it, which does not mean that it is turned into a closed-end fund. Closing an open-end fund means, instead, that no new shares are an offer to investors.43 This is most likely to occur in highly specialized funds, particularly those that invest only in a small country or in a small industry. The typical reason for closing an open-end fund is that the managers, faced with a large inflow of money, cannot find attractive investment opportunities within the fund's scope. Usually, after a lapse of a few months or so, the fund is "reopened." The closing of an open-end fund raises an economic problem of some interest. Once the fund is closed, no new money comes in, but for a variety of reasons some existing shareholders are likely to sell. Consequently, the fund has a net outflow of money, forcing the managers to sell some of their investments. If the fund has sizable holdings in a small country or industry, these sales may in turn depress the price of the remaining investments. This argument suggests that closing a fund may have an adverse effect on the Net Asset Value, but this tentative conclusion needs empirical verification. There is no analogue to "closing" in the case of a closed-end fund, whose managers are not constrained by inflows or outflows of money. However, there is another action that may change the status of a closed-end fund. We saw that sooner or later such a fund tends to trade at a discount to NAV. If the discount becomes large (say more than 15%), the shareholders may decide to turn the

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closed-end fund into an open-end fund, which normally trades at NAV. In the process the management is likely to be fired, and this is one reason why conversions from closed-end to open-end status are infrequent. The managers tend to oppose the conversion and rely on their own holdings, and those of their associates, to block it. Nevertheless, the possibility of conversion serves as a check on possible mismanagement of a closed-end fund. It is also possible that a fund trading at a large discount will be taken over by a better managed closed-end fund. 3.5.1 Money Market Funds

Technically, money market funds are also open-end mutual funds, but the close resemblance of their shares to bank deposits places them in a special category that is kept separate in the statistics. In money market funds (MMFs) the pooled assets against which shares are issued consist of short-term financial instruments such as Treasury bills, commercial paper, and certificates of deposit. Since the prices of short-term securities fluctuate less than those of stocks and bonds, MMF managers attempt to keep the Net Asset Value underlying each share constant, customarily at $1.00 per share.44 To the shareholders, therefore, claims on an MMF are "like money in the bank." This impression is greatly reinforced by the fact that they can draw checks on their holdings, or more precisely on an unaffiliated bank where the fund has an account. Although an MMF is not itself a bank, most shareholders would be hard put to tell the difference.45 The advantage enjoyed by MMFs is that, not being subject to the same regulations as banks, they can offer higher interest rates. During the monetary upheavals of the early 1980s some MMFs paid nearly 20%, whereas banks could then pay no more than 5% on their best checking accounts. As a result, holdings in MMFs soared from $4 billion at the end of 1977 to $220 billion five years later. Since then, falling interest rates have made the MMFs less competitive and shareholdings have grown at a more moderate rate, but they remain substantial with assets of $540 billion at the end of 1994.

3.6 MORTGAGES AND MORTGAGEBACKED SECURITIES

Mortgages (i.e., loans secured by real estate) have long been the main securities supplied to the market by the household sector. They usually have maturities of around 25 years and provide for equal monthly payments that include both interest and reductions of principal. As shown in Section 2.4, nonfinancial business is also a significant issuer of mortgages. The interest rate on a mortgage is usually fixed, but because of recent volatility variable-rate mortgages have become more common. In this type of mortgage the interest rate is revised from time to

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time by reference to some index of market rates. Many mortgages are redeemed in full prior to maturity, in much the same way as a company redeems a callable bond. Since mortgages are tied to specific parcels of real estate, they are not readily negotiable. To overcome this defect, various types of mortgage-backed securities have been introduced. These are generated by pooling mortgages that have been insured by a third party—most often the federal government—against default; mortgage-backed bonds are then issued against this pool. Major issuers include the now private, but originally government-owned, Federal National Mortgage Association (known as Fannie Mae) and two federal agencies: the Government National Mortgage Association (Ginnie Mae) and the Federal Home Loan Mortgage Corporation (Freddie Mac). Although they take a variety of forms, most mortgage-backed bonds (in some cases called "participation certificates" or "pass-throughs") are issued for periods similar to the mortgages that underlie them and carry an interest rate equivalent to the weighted average of the mortgages that make up the pool. The holder of the bond then receives this rate plus a share in the principal repayment made by the issuer of the original mortgage, usually on a monthly basis. The majority of mortgage-backed bonds have fixed coupon rates, although more recently some variable-rate mortgage-backed securities have been issued, based on pools of variable rate mortgage instruments. The main difficulty, paradoxically, in pooling individual mortgages is not so much the risk of default (assuming there is adequate collateral), but the risk of prepayment. If a mortgage carries a high rate of interest, the borrower is likely to prepay it as soon as possible, thus forcing the issuer of a mortgagebacked security to find other (and presumably less attractive) mortgages in which to invest, or to pay off some of the securities. This is why mortgage-backed securities with a high coupon rate are often not quoted at a correspondingly high price: Their expected life is short. Various schemes to overcome this difficulty have been proposed. A recent variation on mortgage-backed securities are known as "assetbacked." Here the collateral consists not of real estate but of such assets as accounts receivable (particularly on credit cards). They exemplify the neverending search for new financial instruments.

3.7 CLAIMS ON FINANCIAL INSTITUTIONS

The wide range of demand and time deposit accounts available at financial institutions (including commercial banks, Savings and Loan Associations, Credit Unions, and money market funds) is an important channel through which funds flow from ultimate savers to those investing in real assets. The majority of these do not give rise to negotiable securities. Nevertheless, there are some important exceptions. Mortgage loans, as has been noted, can be "securitized" (i.e., trans-

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formed into financial instruments). Other examples include certificates of deposit (including Eurodollar CDs), commercial paper, and bankers' acceptances. Certificates of Deposit are issued in units ranging usually from $5,000 to $100,000. They are evidence of title to a time deposit at a bank, frequently with a maturity of 30 or 90 days. Their standardized characteristics make these certificates readily negotiable, and an active market has developed. Their credit standing is equal to that of the bank at which the underlying deposit is held; part of the deposit may be covered by the Federal Deposit Insurance Corporation (FDIC). Eurodollar Certificates of Deposit differ from those just discussed in that they are issued by banks in other countries yet are denominated in U.S. dollars.46 More generally, the term Eurocurrencies refers to CDs issued by a bank in a currency different from its own; thus a Eurosterling CD, denominated in British pounds, may be issued by a Swiss or Japanese bank. Until recently, American banks were not allowed to offer deposits denominated in foreign currencies to U.S. residents, but this prohibition has now been removed. Actually, the abolition of exchange controls in many industrial countries has made the distinction between domestic and Eurodollar CDs largely irrelevant. The market in such CDs has assumed enormous dimensions since it emerged in the late 1950s, to the point where banks in all important countries are now effectively part of one international short-term capital market. Because this highly competitive market is centered in London, the interest rate at which EuroCDs can be sold is known as LIBOR, short for London Interbank Offered Rate. That rate, which is quoted for 1 month, 3 months, and so on, serves as a basis for calculating interest rates on bank loans around the world, so that a borrower may be charged "one and a half per cent over LIBOR." The term commercial paper, or open market paper, refers to short-term promissory notes of standard size issued by large corporations and financial institutions, including the holding companies by which many banks are owned. Typical of the large issuers is the General Motors Acceptance Corporation, which finances automobile purchases. The notes are issued on a discount rather than a fixed-interest basis. In some cases they are "accepted" by a bank, which, for a fee, agrees to repay the holder on maturity in the event of default by the issuing corporation, thus creating a banker's acceptance. Both types are usually issued to finance short-term cyclical working capital requirements. While a significant quantity of commercial paper is outstanding in the United States, not all of it is readily negotiable. In some other countries (notably the United Kingdom), "commercial bills" or "bank accepted bills of exchange," as they are called there, form the main instrument traded in the short-term money markets, but that is not the case here. Some of the factors governing the supply of deposits and financial instruments by banks have already been discussed in Chapter 2. The discussion of corporate financial policy in Section 3.4 is to a large extent also relevant to financial institutions, the principal difference being that the latter have few fixed

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assets or inventories. Accordingly, their main business is rinding the most profitable combination of financial assets and liabilities. This topic is outside our scope. To conclude this section, we return to a financial market, already mentioned in Section 2.5, that is of great importance to banks but in which their customers do not participate: the Federal Funds market, in which commercial banks buy and sell deposits at Federal Reserve Banks. These deposits, it will be remembered, constitute the bulk of the liquid assets backing their liabilities. Trading in the Federal Funds market enables individual banks to match their required reserves fairly closely with daily fluctuations in their liabilities.47 By their nature, Federal Funds are financial instruments with a very short maturity, generally overnight. They are at one extreme of the maturity spectrum.48 Like all fixed-interest instruments, their price is quoted in terms of an annual rate of interest. This rate sometimes changes drastically from one day to the next, or even within the day. Since the daily surpluses or deficits of individual banks tend to cancel out in the aggregate, fluctuations in the Federal Funds rate usually reflect open-market operations by the Federal Reserve. In fact, the daily intervention of the Fed (as opposed to its growth targets for the money supply) is geared largely to the Federal Funds rate, which in turn has an effect on other short-term interest rates because it represents the marginal cost of liquid assets to the commercial banks.

4 The Demand for Securities

Chapter 3 examined securities from the issuer's point of view. Now it is the purchaser's turn. We present a framework, based on economic theory, for analyzing why individuals and other investors are interested in the various types of financial instruments described earlier. Why, for instance, would an individual consider owning government bonds? Why would a pension fund be interested in owning equities? Such questions can be made more precise by replacing the word "why" with "under what conditions." In this chapter we show that the willingness of an investor to hold a particular security depends on two sets of characteristics: those of the investor and those of the security. The principal characteristics of securities—particularly the time pattern of returns, the risk of default, and the negotiability—are discussed in the Chapter 3. How to characterize the behavior of individual investors is the topic here. There are two fundamental reasons why individuals demand securities either directly or through some form of financial intermediary such as a mutual or pension fund. The first is that their pattern of income over time differs from their desired sequence of consumption. By holding financial assets, the pattern of cash receipts can be rearranged so as to synchronize it with the pattern of spending needs.1 Investment in securities as a means of providing for retirement or saving for the purchase of an automobile are common examples. Each purpose requires a different timing of investment, return, and redemption of principal. One major group of attributes of interest to those demanding securities, therefore, are those relating to timing: the maturity and liquidity characteristics of a security as well as the degree to which it offers opportunities for regular withdrawal of cash or reinvestment. 78

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The second major reason for demanding securities stems from the desire to increase total dollar wealth. Sometimes this reflects an "aggressive" attempt to increase individual net worth through successful speculation. For other investors it is essentially a "defensive" attempt to maintain the purchasing power of their savings in the face of rising prices. These different objectives, and the different degrees of risk aversion that underlie them, give rise to variations in demand for securities according to their risk and expected return characteristics. In this chapter we begin by examining the underpinnings of demand for securities in terms of these three basic attributes: time characteristics, expected return, and risk. The remainder of the chapter is devoted to what might be termed the "portfolio complication." Here we introduce a concept that will appear a number of times throughout this book because it has revolutionized thinking about the evaluation of securities since the late 1950s. It centers on the realization that the correct measure of one of the most important attributes of a security, namely its risk, will differ depending on whether it is viewed in isolation or as part of a portfolio. Since this is the case, we need to consider the structure of an investor's entire portfolio even to define the relevant attributes of a security. Portfolio relationships therefore become the key to understanding securities demand.

4.1 THE TIME DIMENSION

In Chapter 2 we examined some of the macroeconomic relationships involving the demand for securities, mostly at the empirical level. It is now time to explore the microeconomic theory relevant to that demand. The focus is on a problem that is important to most people, namely, saving for retirement. This objective is also important for the financial markets because it is a major source of funds, either directly from individual investors or indirectly through pension funds or life insurance companies.2 Uncertainty is disregarded in this section; it is taken up in Section 4.2. 4.1.1 A Case in Microeconomics: Saving for Retirement

To keep the exposition simple, take the case of an individual (Adam) who starts his working life on his twenty-fifth birthday. He considers his remaining life in terms of two periods: the first being his working years (assumed to be fixed at 40), and the second a period of retirement of unknown length. Uncertainty about the length of the retirement period can in principle be eliminated by buying an annuity. This is a contract, usually made with a life insurance company, under which the individual pays a lump sum immediately and in exchange receives a fixed amount per year or month as long as he or she lives.3 We suppose, therefore, that on his sixty-sixth birthday (when he retires) Adam buys an annuity

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THE DEMAND FOR SECURITIES

that provides a fixed income per year until his death. The possibility that Adam wants to leave an inheritance to his dependents, or a charitable bequest, is disregarded; so are other complications such as taxation, inflation, and contractual saving (e.g., through an employer's pension fund). During his working life Adam is assumed to earn a fixed amount of $20,000 per year, payable at the beginning of each year. In the present context, the basic decision Adam has to make is how much of his earnings he will consume during his working life, the balance being saved for consumption in retirement. This choice can be analyzed by means of the utility function, one of the main tools of microeconomics. The utility function serves to represent an individual's preferences for various alternatives. Thus if x and y are two levels of wealth, and u(x) and u(y) are the utility levels associated with them, then u(x) > u(y) means that the individual prefers x over y.4 With his savings Adam purchases securities whose annual return r is assumed to be certain and constant over time. An investment of $1 now will be worth $(1+r) one year from now, and $(1+r)40 in 40 years. Thus if Adam saves an amount of st in year t of his working life (where t runs from 1 through 40), then his accumulated savings on his sixty-sixth birthday will be

With these accumulated savings Adam buys an annuity that will pay cA at the beginning of each year until he dies.5 The fraction c, which is supposed to be known in advance, depends on the rate of interest and Adam's life expectancy at age 66. We now introduce a further simplification, namely, that Adam saves the same amount each year. Since it was earlier postulated that his earnings remain constant during his working life, this is not implausible; the question whether it is optimal cannot be addressed here. Algebraically this means st = s for all t, and the displayed equation becomes

The expression in braces on the second line is a geometric series whose sum can be found in elementary algebra texts:

For instance, with r =.05 (corresponding to an annual interest rate of 5%) the sum amounts to 120.8, meaning that a person who saves $1 per year will have $120.80 after 39 years. Of this total, $40 is original investment and $80.80 is accumulated interest. From the penultimate equation we then see that on his

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sixty-sixth birthday Adam's savings of $.s per year will have produced assets (A) of (1.05)(120.8)s = 126.84s dollars. So far the value of s has not been specified. We need one additional item of information to discuss s meaningfully. This item is the constant c, which determines annual annuity payments from a given purchase price A. Suppose c = 0.1, which means that the annual payments are 10% of the purchase price. It follows that these annual payments equal $12.684s. Thus, annual savings of $2,000 would imply annual annuity receipts of $25,368, more than Adam earned during his working years. Depending on his utility function this may be the pattern he prefers. It should be borne in mind, however, that after retirement there is no further need for saving under our assumptions, so all of the $25,368 is available for consumption compared to $18,000 (earnings less savings) during Adam's working years. It is of interest to explore an alternative lifetime pattern, in which consumption is constant throughout. Putting annual earning for convenience equal to y, we then find that y — s= 12.684s, which implies s = 0.073y, or savings are 7.3% of earnings. Despite the many simplifying hypotheses, this is not an implausible figure. With his assumed earnings of $20,000 Adam would then save $1,460 during each working year, leaving $18,540 for consumption. The reader can also verify that is approximately equal to consumption during retirement, the small discrepancy being attributable to round-off errors. What we have developed is a bare-bones application of the "life-cycle" theory of saving. This theory is mostly due to Franco Modigliani, who later received a Nobel prize for his work. It has important implications for the individual's demand for securities.6 Since most saving for retirement involves a long-term commitment, the theory clearly points to investment in long-term securities such as equities and long-term bonds. In this connection, recall the yield curve mentioned in the Chapter 3—and reconsidered later in the present one—according to which short-term bonds normally yield less than long-term bonds. A person who is planning for retirement would not normally be interested in short-term securities. We already know, however, that there are many types of securities, each with their own price, rate of return, and other characteristics. The next issue to address, therefore, is the relationship between rate of return and security prices. 4.1.2 Present Value and Duration

In the preceding section we did discuss the allocation of savings between alternative investment opportunities, nor shall we do so here. We can say, however, that in order to be willing to invest in a particular security, Adam would require a total rate of return of r per annum. What price would he then be willing to pay for a security that returns $F1 in year 1, $F2 in year 2, and so on for 5 years with return of the principal invested II on maturity? Ignoring the risk for the present, the answer is the "present value" of that security, calculated as follows:

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The present value (PV) formula reflects the fact that a return in the future, which can only be used or reinvested when it is received, is worth less than a return now. Hence future returns must be "discounted" by the required rate of return. The value we place on future returns (payoffs) by this process is equal to the amount we would have to invest now at the required rate r in order to generate that payoff in the future. More generally, if the required rate of return is allowed to vary over time, the general form of the PV formula becomes

Alternatively, the dollar payoffs and the required rate of return may both be constant but continue into perpetuity. Using the formula for the sum of an infinite geometric series, the present value then turns out be simply

Thus a preferred stock in a top-rated company (i.e., one whose risk of default is negligible) paying $2.00 per year would have a present value of $40 if the required interest rate is 5%. Let us now relate this PV concept to some other specific types of securities. Recall that the PV is equal to the current price we should be willing to pay. Consider, then, a $1,000 bond issued with an annual coupon rate of rc and a maturity of 3 years. Its PV is

The required rate of return in this case must be equal to the rate available on new issues of an equivalent bond. On the day of this bond's issue, therefore, r is equal to the coupon rate rc, so the PV becomes: By performing a little algebra, the reader can be convinced that the bond's PV on its day of issue is equal to its face value, as one would expect. Next, suppose that bond rates rise immediately after the issue. If our bond has a coupon of 10% and rates rose to 15%, its PV would then be:

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In other words, a rise in bond rates causes the price of outstanding bonds to fall, and the holder to suffer a consequent capital loss. Conversely, declining bond rates produce a capital gain on existing bonds. It should also be clear that the longer the bond's maturity, the more its price will be influenced (r appears more times and with higher power in the denominator of the PV formula the longer is the maturity). In this sense, therefore, longer bonds have a higher risk than short bonds. In fact, however, the simple "term" of the bond (i.e., its years to maturity) is not always the relevant measure of maturity for pricing purposes. Consider the case of two bonds each with 10 years to maturity; one is a "coupon" bond paying 10% interest per annum and the other a "zero-coupon" bond (see Section 3.2.1) paying only the principal at maturity. Will the price of one be more strongly affected by changes in interest rates than the other? The answer is clearly "yes" because some of the coupon bond's return comes in the early periods, hence this part of its value is in effect "short-term" despite the long maturity of the overall bond, and so is less influenced by interest rate changes. To account for these differences a statistic known as duration is computed. In contrast to simple maturity it provides a measure of the true "timing attributes" of a bond. Duration is calculated by taking the maturity of each payment the bond returns to its holder (e.g., the maturity of the second annual interest payment is 2 years) and multiplying it by the percentage of the bond's present value paid out at that maturity. It is thus a weighted average of the different maturities represented by the coupon and principal repayments associated with the bond. More formally:

where DUR is the duration, FV the face value, PV the present value, and t time in periods (years if interest is annual, quarters if it is quarterly, etc.). The final value of DUR is thus a "corrected" maturity with the same periodicity as t, usually years. Shares, of course, also have important time-related attributes. The price an investor is willing to pay for a share may be expressed in terms of the following present value calculation:

where divi is the dividend paid in each time period, IIn the market value of the share at the end of the investor's desired "holding period" or investment horizon, and r0 the required rate of return.7 A great deal of care must be taken in the interpretation of this formula.8 Superficially, it might appear that an increase in the current dividend payout will

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necessarily cause the share price to rise. In fact, such an assertion is often completely unjustified because the size of future dividend payments (div2, div3, etc.) will depend on the rate at which earnings grow. So long as the firm has profitable9 investment opportunities open to it, the more earnings it retains and reinvests, the faster its future earnings will grow, and the larger will be its potential for future dividends. Paying out higher dividends now reduces the funds available for reinvestment. Current dividends therefore tend to reduce the unit value of the firm's shares in the periods following the payout. If these funds are not replaced from other sources, or if alternative sources come at higher cost, the total value of the firm's shares may fall. These interactions become more transparent when we write out the present value formula for a share in full, rather than the summarized form given above:

where dt = the dividend payout ratio (i.e., dividends over earnings) in period t; e = the rate of return the firm earns on its assets; and A = total assets per share. Now assets per share in the future will depend on current retained earnings and the amount of funds raised externally in the financial markets through the issue of new securities by the firm. Thus

where RE = earnings per share retained in the period and NI = new funds raised externally and invested (per share) in the period. Therefore

Suppose, then, that we compare the shares of two firms that are identical except that one (firm X) pays all of its first year's earnings out as a dividend and the other (firm Y) does not pay a first-year dividend at all. Neither raises any new capital, and they are both liquidated at the book value of their assets at the end of 2 years. The respective present values of a share in each are then

Since the amount of retained earnings in firm Y is RE 1 e 1 A 1 , the difference in present value per share is

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Now d2= 1 in both cases, since the firms are liquidated at the end of the second year, thus:

an expression that will be negative so long as e2 > r. In other words, the current value of a share in the firm with the higher dividend payout is less than the firm with no dividend payout so long as its rate of return on assets exceeds the minimum required rate of return r. This condition defines "profitable" opportunities for reinvestment. A firm that has such profitable opportunities available to it will increase the unit price of its share the higher the percentage of earnings it retains. For example, IBM and Xerox, which did not pay any dividends at all for a number of years after their formation, still enjoyed strong increases in their share prices because both had opportunities for reinvestment at very attractive expected returns. Consider the intuition: As an investor, would you rather that these companies paid out the funds in dividends or reinvested them in their high-yielding industries? Perhaps contrary to your intuition, the answer is actually that, except for the transactions cost and personal taxation implications, you should not really care. The reason is quite simple: If the firm retains its earnings, then the price of your existing shares will rise. If, instead, they pay out their earnings in dividends and issue more shares to finance their investment needs, the price of your existing shares will not rise as much, but you can use those dividends to purchase more shares. In each case, the value of your investment increases by the same amount. This observation leads to a very significant conclusion—namely, that the timing of a firm's earnings matters for its present value but the timing of its dividend payments does not (provided it has profitable investment opportunities). We illustrate with the following example. Suppose a firm has a present value of $100 million and 10 million shares outstanding, and it decides to pay out $10 million in dividends. The share price will therefore fall from $10 before the dividend has been paid to $9 after the dividend payment, given that its total present value is now only $90 million. The holder of 90 shares would then have a total of $810 worth of shares and cash. This compares with $900 worth of shares before the dividend. To maintain its total assets, however, the firm must issue $10 million worth of new shares at the market value of $9 each. If you then use your dividend to

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purchase 10 additional shares, your holding will increase to 100 shares at $9 each, maintaining the total value of your investment at its original $900. According to this argument, then, it makes no difference whether the company pays a dividend and issues more shares, or retains its earnings, so long as the sum total assets are being supported under both options. In practice, however, there are three reasons why the value of your investment may in fact change and hence the firm's dividend policy may alter the attractiveness of its shares to you, the investor. The first reason stems from the taxation implications. In most countries, including the United States, the rate of personal taxation on long-term capital gains has often been less than that on dividends.10 In the case of securities held directly, therefore, a stock with high retention of earnings would then be preferred to one with high dividend payout on taxation grounds. If this were true for a majority of investors, demand for low dividend payout stocks would increase, causing their prices to rise relative to high payout stocks. Some investors, however, notably life insurance offices and pension funds, are taxed on capital gains but not on dividends. As a result, the overall response of demand to different dividend payout levels is unclear. Obviously the dividend payout characteristics will affect the particular "clientele" of investors attracted to a stock, but the net effect on its price is uncertain. The second reason concerns the potential effect of transactions costs. On one level, the company with a high payout policy faces costs (often quite substantial) of mounting the issue of new securities necessary to maintain an asset level equivalent to that of the low payout company (including legal and underwriting fees). This extra cost, in turn, reduces the total value of the firm and hence its shares. In addition, the investor may face various costs in handling the dividends and resubscribing the proceeds to a new issue, or buying additional shares to maintain the total investment on the open market. Transactions costs on both sides, therefore, reduce the demand for high payout shares. On the other hand, to the extent that investors seek a regular income from their securities, payment of dividends might reduce an investor's transactions costs by avoiding the necessity to sell a portion of the shares at regular intervals so as to provide the desired cash flow. The third reason pertains to the possible "information content" of dividends. In this connection it is often argued that the declaration of an increased dividend provides positive information to the market about a company's performance and the managers' confidence in its future. To the extent that investors did not previously recognize the firm's success, the demand for its shares and, hence, their price might be expected to rise in response to this dividend "signal." While this argument is often raised, it is not altogether convincing. For one reason, as noted earlier in this section, an increased dividend payout may signal the lack of profitable new opportunities in which to invest earnings, rather than successful performance. Overall, therefore, while a number of complications do exist, it seems that our basic conclusions regarding the "time attributes" of shares remain fairly ro-

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bust—that is, while the timing of a firm's earnings pattern is a crucial attribute in the determination of demand for and price of its shares, the timing of its dividend payments are of considerably less, possibly even little, relevance as an attribute of the share. 4.1.3 The Calculation of Yields on Zero-Coupon Bonds

Until now, all the formulas presented have been in terms of years, which is to say they assume "discrete" time intervals. This assumption limits the usefulness of the formulas because it makes it difficult to calculate the present value or the return on a Treasury bill that matures 68 days from now.11 For many purposes it is easier to operate with "continuous" time rather than with discrete intervals. This approach requires a little more mathematics, but the resulting gain in simplicity makes the work worthwhile. The key concept in the continuous-time approach is exponential growth or decline. Elementary calculus tells us that if

where t is time as before, then

Here y'(t) is the derivative or rate of change (over time) of y, and the whole left-hand side of Equation (4.2) may be interpreted as the "proportionate rate of change," which has the value b irrespective of time. It is quite possible for b to be negative, indicating decline rather than growth. We shall see in a moment that b is closely related to the rate of interest, which can also be negative.12 It should be clear that Equation (4.1) can be written

where the logarithm is understood to be "natural" (that is, with e = 2.71828 . . . as base). Since natural logarithms are available on most calculators, the last equation is convenient for numerical applications. Equation (4.3) implies that if y is observed at two different times then

As an illustration we consider the yield on zero-coupon bonds, a category that includes Treasury bills (as explained in Chapter 3).13 Suppose a T-bill maturing 68 days from now is quoted at 98; what is its yield? More precisely, at what annual interest rate does a sum of $980 have to grow so as to become $1,000 in 68 days?14 To answer this question, we first calculate that 68 days is 0.1863 years, and that log(1000)-log(980) = 6.9078-6.8876 = 0.0202. Equation (4.4) can then be solved for b by dividing 0.1863 into 0.0202, the solution

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being 0.1084. This number is not yet the annual interest rate we seek; it is merely a proportionate rate of change that is independent of the time unit. The annual interest rate can be calculated by considering the growth of y over a finite period of time, in this case 1 year. In Equation (4.4) put tl =0 and t2= 1, thus obtaining the change in log(y). Taking exponentials and dividing by y, we get the proportionate increase or decrease in y over 1 year, which is the annual interest rate on T-bills:

In the current example this means rT = 0.1145, not very different from b. Thus a T-bill maturing in 68 days and priced at 98 has a yield of 11.45%. At this point a warning is in order. The reader who looks up the yield on a T-bill or other zero-coupon bond in the newspaper may well find a figure that is slightly different from the one calculated by our method. Indeed, if he looks at a second newspaper he may find yet another figure. It appears that several ways of calculating yields are in use, all of them based on special (and usually unstated) assumptions and producing somewhat different results. The method presented here, recommended also by the more sophisticated texts on finance, does not depend on any special assumptions. In the following section it is applied to a comparison of the yield on zero-coupon bonds of varying maturity. 4.1.4 The Term Structure of Interest Rates

In Chapter 3 we presented "yield curves" for Treasury obligations of different maturities. The relation between yield and maturity expressed by such curves is known as the term structure. Based on Federal Reserve estimates, the curves of Chapter 3 reflected the prices quoted for coupon bonds. A Treasury coupon bond, as shown in Chapter 3, is a stream of payments scheduled every 6 months until the bond is redeemed. It is therefore equivalent to a bundle of zero-coupon bonds maturing at differing times, all but one of which represent interest while the remaining ones represent the principal. In Section 4.1.3 a method for calculating yields was applied to a zerocoupon bond. The question arises whether this method can also be applied to a coupon bond, and the answer—except in certain special cases of little interest— is "no." The method consists of determining a constant growth rate that will lead from the initial investment to the ultimate payoff. In general there is no constant growth rate for a sequence of zero-coupon bonds maturing at different times; instead there will usually be a different growth rate for each maturity, and any attempt to average these growth rates in some fashion is inherently arbitrary. This may seem a serious drawback of the continuous-time approach of Section 4.1.3, but actually it agrees with reality. At the end of that section we referred to the special assumptions made in calculating yields on coupon bonds.

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One such assumption is that interest receipts are reinvested in the bond itself; this assumption implies, among other things, that an 8% coupon bond due in 20 years and trading at par (100% of the face value) has a yield of 8%. This implication may at first seem eminently plausible, but actually it is nearly always false because of the term structure, which says that yield depends on maturity. In general, when interest is received on a coupon bond it cannot be reinvested in the same bond at the same interest rate, because at that time the bond is no longer a 20-year bond but one of shorter maturity.15 If the yield curve is "normal"—that is, upward sloping—the yield upon reinvestment will be less than 8%; if the curve is "inverted," the yield will be more. It is only when the yield curve is completely flat that the special assumption just analyzed is valid; this is the uninteresting exception alluded to earlier and subsequently acknowledged by such qualifiers as "generally" or "nearly always." Thus we are led to conclude that the most meaningful yields are those on zero-coupon bonds.16 The conventional yield curves for coupon bonds presented in Chapter 3 are, strictly speaking, incorrect and should be replaced by those calculated from the prices of zero-coupon bonds. Until recently this calculation was difficult because price quotations on "zeros" were hard to obtain.17 Now such quotations are published daily in financial newspapers, and they are used for three recent dates given in Figure 4.1.

Figure 4.1 Yield curves for zero-coupon bonds. Note: Only November maturities are shown. Source: Calculated from prices in the Wall Street Journal (Annual Review in first issues of 1990, 1994, and 1995) using the method given in Section 4.1.3. For the earliest date, the prices reflected last trades; for the later dates, they are averages of bid and ask prices. The yields given in the source were not used because they appear to have been calculated by different methods.

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The patterns revealed by Figure 4.1 are not greatly different from those shown in Chapter 3 for coupon bonds. The earliest yield curve, somewhat jagged because it reflects actual trades that are not necessarily simultaneous, is slightly inverted but close to being flat. The curve for the end of 1993 shows a marked difference between the yields on short and long maturities, at least up to about 20 years from the present; the yields for very distant maturities are lower again.18 Note also that at the end of 1993 the nearby maturities had a much lower yield than at the previous date, but that the long-term yields did not change as much. Thus the 1993 curve was much steeper than the 1989 and 1994 curves, which reflected tight monetary policy; the 1993 curve exhibits a "normal" pattern.

4.2 THE RISK DIMENSION

Many investors have traditionally thought of risk only as a characteristic of the so called "speculative securities" such as shares or futures contracts. In fact, risk is a characteristic of virtually every type of investment available in the market. Even a checking deposit with a federally insured bank involves a risk, the risk that the real purchasing power of that deposit will be eroded by an uncertain rate of inflation. Such a pervasive element in the demand or securities clearly requires explicit recognition in our analysis. To make this possible, however, we need some way of satisfactorily quantifying the risk such that it can be manipulated along with other measurable parameters such as interest rates or securities prices. We achieve this quantification by expressing risk in terms of probability theory.* 4.2.1 The Measurement of Risk

To begin with, we need a method for analyzing risk. Such a method is provided by probability theory, which may be described as the mathematics of uncertainty. Probability theory had its origin in the study of games of chance, but it was soon applied to more important topics19 and is now used in virtually every field of science. The basic concept is the probability of one outcome in the context of a given set of possible outcomes. Thus, if a fair die is thrown there are six possible outcomes, and the probability of getting a "three" is one in six. In this simple case the six outcomes may be called "elemental" in the sense that they cannot be easily explained in terms of more basic causes.20 The calculus of probabilities is especially concerned with "composite" outcomes, such as getting an even number of points with one throw, or two "threes" in two successive throws. These composite outcomes are combinations of elemental outcomes.21 The calculus of probabilities provides rules, which need not concern us here, for deriving the probabilities of composite outcomes from those of elemental outcomes. * Readers familiar with elementary probability theory may skip the next section.

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In the study of risk we are especially concerned with outcomes that have numerical values, the outcome values for short. Usually these outcome values will be positive or negative amounts of money. An outcome value is a random variable, an ordinary variable whose values corresponds a certain probability. Thus, in throwing a fair die the probability attached to each of the elemental outcome values 1,2, . . . 6 is one-sixth, but if the die were not fair, the probabilities would be different. In any case, the probabilities must satisfy two conditions: They must be nonnegative and if they are summed over all elemental outcomes their sum must be one. Suppose you bet $10, double or nothing, on the toss of a fair coin. There are clearly two possible outcomes: Either you lose $10 (the probability of which is 50%, the chance of your chosen side facing down) or you win $10 in addition to the return of your $10 original stake (again with probability of 50%). If you continued to enter such a wager with everyone you met, how much would you expect to take away with you at the end of the day? The answer is, of course, $10.22 This result can be shown mathematically by taking the expected value (EV) of the wager, which is equal to the sum of all possible outcomes (in dollars), each multiplied by its respective probability.23 In this case we have: EV = $20 x 0.5 + $0 X 0.5 = $10. The idea of a random variable is central to probability theory. Closely related is the concept of a probability distribution, which is a function Prob(x) defining the probability p corresponding to each outcome value x. In the examples used so far there is only a finite number of x's, but it is often more interesting to consider a continuum of possible outcomes. For instance, the temperature at noon tomorrow may be considered a continuous random variable. The probability distribution for a continuum of outcomes is defined in much the same way as it was in the case of a finite number of outcomes.24 The outcomes x whose probability is defined by Prob(x) need not be elemental, but they must be mutually exclusive and exhaustive. From any sample of observations, or from any given probability distribution, certain important numbers called descriptive constants can be calculated. The best known descriptive constant is the mean or expected value, defined as the sum of the numerical values (outcome values) of all possible mutually exclusive outcomes each multiplied by its probability, or by its relative frequency in the case of a sample. Consider a lottery in which each ticket has a 1% probability of winning the only prize of $500. There are only two mutually exclusive outcomes, with numerical values of 500 and 0, respectively.25 The expected value of the ticket is m1(x) = 0.01 x $500 + 0.99 x$0 = $5.00.

(4.6)

The reader is encouraged to verify that in the dice-throwing example the expected value is 3.5. The mean belongs to a class of descriptive constants known as moments; in fact, it is sometimes called the first moment and the preceding notation reflects

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this terminology.26 The second moment differs from the first only in that the outcome values in the first—but not the probabilities—are squared. Thus, for the lottery we get m2(x) = 0.01 X 5002 + 0.99 x O2 = 2500.

(4.7)

It will be seen that the second moment is the expected value of x2. A related concept, the variance, is actually more useful. To calculate it, each of the outcome values in Equation (4.7) is first reduced by the mean.27 Consequently var(x) = 0.01x(500-5)2 + 0.99x(0-5) 2 = 2475.25.

(4.8)

As is shown in every beginning statistics textbook, the variance can be more easily computed from the formula var(x) = m2(x)-{m1(x)}2.

(4.9)

Finding the variance in the dice-throwing example is again left as an exercise. The variance is important as a measure of the dispersion of the outcome values. We can see why this is so by looking at a case where all the outcome values are the same, which obviously implies that each is equal to the mean so that the variance is zero. In the lottery example the outcome values are very different and the variance is many times larger than the mean. Strictly speaking, though, the mean and the variance are not comparable because they do not have the same dimension (dollars for the mean, dollars squared for the variance). This defect can be overcome by taking the square root of the variance to obtain the standard deviation, usually denoted by a. In the lottery example, is about 49.75, still much larger than the mean. In the dicethrowing case, on the other hand, is about 1.71, less than half the mean. However, the means in the two examples are different. To ensure comparability, it is customary to divide the standard deviation by the mean; the result is called the coefficient of variation. The respective values for the two examples are 9.95 and 0.49. Since the coefficient of variation does not depend on the units of measurement, it is the simplest indicator of the relative riskiness of different investment prospects. By this criterion, the lottery is about twenty times riskier than throwing dice. Of course, the lottery used as an example was hypothetical, but actual lotteries probably have even larger coefficients of variation, especially if they include "megabuck" prizes. It should also be pointed out that so far nothing has been said about the cost of participating in these games of chance. There are also moments beyond the second, of which we at present consider only the third. By now it should be clear that the third moment is calculated by raising the outcome values to the third power, and that it is desirable to subtract the mean from the outcome values. The result is called the third moment "around the mean" and indicates the asymmetry, or skewness, of the probabilities of the

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elemental outcomes. In throwing dice, for instance, favorable outcomes (those above the mean) are just as likely as unfavorable ones; the outcomes therefore have symmetric probabilities and the third moment around the mean is zero, as the reader may like to verify. By contrast, the outcomes of the assumed lottery are highly skewed: a small probability of winning the prize and a large probability of getting nothing. The third moment around the mean is approximately equal to 9.85.28 Because this value is greater than zero, the distribution of the outcomes is said to be "positively skewed"; negative skewness could mean a small probability of a very unfavorable outcome and a large probability of an outcome whose value is slightly above the mean. An example is owning an uninsured house, where the unfavorable outcome corresponds to a fire. 4.2.2 Bivariate Distributions

So far we have considered only one random variable at a time. In the analysis of risk it is often desirable to consider more than one random variable, for instance tomorrow's prices of two securities. The definition of a probability distribution can easily be extended to the case of two or more random variables; when there are two, for instance, we write Prob(x, y), where Prob(x, y) is a bivariate probability distribution. One may think of a bivariate distribution as a univariate distribution in which the outcomes are all possible (and mutually exclusive) combinations of the outcomes in each random variable separately. Consider an individual who owns two tickets in the same lottery. There are now three outcomes with positive probabilities: Ticket no. 1 wins the prize (x = 500,y = 0), ticket no. 2 wins (x = 0,y = 500), and neither ticket wins (x = y = 0). 29 From the elemental outcomes, of which there are 100 as before, it is clear that Prob(500,0) = 01,

Prob(0,500) = 01,

Prob(0,0) = 98.

(4.10)

The expected value of ticket no. 1 is given by (m 1 )(x) = Prob(500,0) x $500 + Prob(0,500) x $0 + Prob(0,0) x $0 = $5.00,

(4.11)

just as in Equation (4.6). It can easily be verified that m1 (y) also equals $5.00. When there are two or more variables, the relations between them are obviously of interest. The covariance, a concept that has no counterpart in univariate distributions but also belongs to the class of moments, can often be used to describe these relations. It is defined as the expected value of the product of two random variables, each of them reduced by its respective mean (just as for the variance.) In formula: cov(x, y) = m 1 {x-m 1 (x)}x{y-m 1 (y)}.

(4.12)

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Applying this formula to the lottery example we get

Since the covariance, like the variance, depends on the unit of measurement, it is again desirable to introduce a dimensionless counterpart. This is the correlation coefficient, defined by

The variance of x in the lottery example was calculated in Equation (4.8), and in this case var(y) obviously has the same value. Therefore

The negative correlation reflects the fact that ticket no. 1 and ticket no. 2 compete for the same prize, but the correlation is very small because neither ticket has much chance of winning.30 Using the idea of a probability distribution and its related moments, it is then possible to define the risk of a wager relative to this expected value. If we have a 100% probability of achieving an outcome very close to the expected value, then the wager has a low risk. The larger the range of possible outcomes and the more dispersed across these possibilities the probability becomes,the greater is the total risk. A simple illustration is provided in Figure 4.2. Both investments have an expected value of zero (in other words, on average they

Figure 4.2 Probability and risk of securities

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will both break even), but the risk of B (the investment with a much greater dispersion of probable outcomes) is considerably higher than that of A. Let us now take one more step toward reality. Suppose that the expected values of the two investments are unequal so you are faced with deciding how much you would be willing to pay for either of the two securities C and D shown in Figure 4.3. Security D has some attractive possibilities for high profits and a higher expected value. At the same time, it has a long tail of sizable potential losses from which the investor in security C is protected. On the other hand, while the return on security C is less volatile, it has a lower expected value. Many real world investment decisions are like the one shown in Figure 4.3. A higher expected return often comes only at the expense of higher risk and vice versa. What we require, therefore, is some way of measuring the rate of tradeoff which an investor considers acceptable; that is, how much extra expected return is required to render an investor willing to accept an additional unit of risk? The major body of work that has proved useful in tackling this problem is the theory of expected utility. 4.2.3 Expected Utility

The roots of the expected utility theory go back as least as far as Czarist Russia and its passion for gambling, to a puzzle that has become known as the "St. Petersburg Paradox." The problem was as follows. Suppose you are offered $2 if heads comes up on the first toss of a fair coin, $4 for two heads in a row, $8 for three heads in a sequence, $16 for four heads, and so on. You are permitted to keep your winnings on all previous throws. However you are "knocked out"

Figure 4.3

Probability and risk—unequal expected values

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of the game the first time tails comes up. How much would you be willing to pay to have the opportunity to play this game? As a starting point, let us look at the expected value of the St. Petersburg game for an arbitrary number of throws: EV=1/2X2 + 1/4X2 2 +1/8X2 3 + . . . +1/2nx 2n. The probability of three heads in a row, for instance, is (1/2 x 1/2 x 1/2) for a payoff of 23. Evaluating the expression as n goes to infinity we get EV= 1 + 1 + 1 + . . . = . Not surprisingly, there are few takers, even in a gambling community, at an infinite price, yet that is the expected value of the game. The paradox can be resolved by observing that for most individuals the marginal utility they derive from an additional $1 of wealth declines as their total wealth increases. Put another way, $1 means more to you when you have only $10 to your name than it would if you were already a millionaire. Consider throw number 21 in the St. Petersburg game. Its expected value is $1, but would you pay an extra $1 now for the chance to win approximately $2 million with a probability of (1/2,000,000) when you might be "knocked out" on the first throw and it has already cost you a great deal to play? The answer for most people is "no"; they may be willing to pay something but not as much as $1 extra. Clearly, to take this into account we need to calculate the expected value of the utilities of the possible payoffs, not just their dollar values: in other words the expected utility: EU=1/2U(2) + 1/4U(4)+ . . . + 1/2 n U(2 n ), where U(x) represents the utility of a payoff of $x. Now a new question poses itself: What is the appropriate utility function to use? Utility functions fall into three main categories depending on the behavior of marginal utility as wealth increases. These are illustrated in Figure 4.4. Diminishing marginal utility of wealth (i.e., each additional dollar of wealth provides less additional utility than its predecessor) is associated with risk aversion. Constant marginal utility of wealth means that the investor is risk-neutral, while increasing marginal utility of wealth is associated with risk-loving behavior. A risk-neutral investor will be prepared to purchase a share in a risky investment at its expected value. Risk averters will only purchase a risky investment at a discount below its expected value because the associated risk has a negative utility that offsets some of the positive worth of the expected return. Risk lovers, on the other hand, will be willing to pay more than the expected value in order to have the chance to participate in a risky venture. It is possible, of course, that any individual will exhibit all three of these attitudes toward risk over different ranges of wealth. Friedman and Savage (1948), for example, pointed out that it is common for a single individual to buy both lottery tickets and insurance. Since the institution running the lottery takes a percentage of the total pool, lottery tickets cost more than their objective ex-

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97

Figure 4.4

Utility and risk preference

pected value. Their purchase, then, may be an example of risk-loving behavior.31 Yet the same individuals who buy lottery tickets clearly show risk aversion when they insure themselves against a potential loss from fire instead of simply accepting the uninsured expected value. It appears, therefore, that when the size of the loss relative to total wealth is small and the possible winning large (even at a very low probability), many people act as risk lovers. Conversely, when the potential loss of total wealth is large, even at relatively small probability (such as a household fire), people are risk-averse. An alternative explanation is that although people are generally risk-averse across the entire wealth range, they believe that the probability of winning in the case of a lottery (i.e., their subjective probability) is much higher than the objective odds. In this case the "expected value," based on subjective probability, is actually above the cost of the ticket and hence their behavior is consistent with risk aversion. In any case, since risk-averse behavior is the most common trait observed in practice, it is the main focus of attention in the analysis that follows. We should begin, therefore, by defining it with slightly more precision. As we have seen, an individual is defined as risk-averse if he or she is willing to pay less for a risky investment than its expected value (assuming probabilities can be objectively determined and are equal to the investor's subjective probabilities). The maximum amount an individual is prepared to pay for a risky investment, in turn, should be such that the utility of the cash given up in purchasing the security is just equal to the expected utility that that security provides. In other words, the dollar value of a security is equal to the dollar value of its expected utility.

98


Figure 4.5

Risky investment valuation by the risk-averse investor

Not surprisingly, this amount is termed the certainty equivalent of that security, the number of certain dollars "in the hand" that the investor is prepared to give up in order to acquire the prospects for return offered by the security. The difference between the expected value of the security and its certainty equivalent is then the risk discount, the discount an investor requires in order to exchange certain dollars for expected, but risky, dollars. We illustrate with a simple example. Suppose your total wealth is $200,000 and you have the opportunity to invest all of it in a joint venture. If successful, the venture will increase your wealth to $5 million; if it fails, however, you will lose $100,000. The probability of success is 50%. The expected value of this investment is then: EV = 5,000,000 x 0.5 + 100,000 X 0.5 - 200,000 = 2,350,000. Thus, if you were risk-neutral you would agree to participate since the expected value is positive. In fact, you would be willing to pay an additional $2,150,000 to participate. Let us suppose, however, that you have a utility function of the form: U(x)= log x, where x is your level of dollar wealth and log is the natural logarithm, already encountered in Section 4.1.3. As is clear from Figure 4.5, this utility function exhibits diminishing marginal utility of wealth, hence risk aversion. In this case the expected utility of the investment is: EU = 0.51og(5,000,000) + 0.51og(100,000)-log(200,000) = 7.71+5.76-12.21 = 1.26.

99

THE RISK DIMENSION

In other words, the expected utility of the investment is equal to the utility levels associated with each of the possible outcomes multiplied by their respective probabilities, less the utility of the certain $200,000 or current wealth you would be giving up. Once we have this expected utility we can calculate the amount in dollars the investment opportunity is worth to the risk-averse investor by taking the certainty equivalent. This is equivalent to finding the x such that logx = EU, which may be written as in our example—that is, the exponent of expected utility. In other words, an individual with a log utility function would only be prepared to pay $3.53 for the investment opportunity above. The risk discount (RD) is then equal to the expected value (EV) less the certainty equivalent (CE): RD = $2,350,000-$3.53 = $2,349,996.47. The reason for this huge discount is the high disutility of losing $100,000 (half of current wealth) and the low marginal utility associated with the high dollar gains. The preceding discussion of utility functions may raise a suspicion among many of our readers that we have entered the world of economic esoterica, beyond which only insanity lies. You are assured, however, that our feet remain firmly on the ground. To make good that assurance and in the process to demonstrate the use of an actual utility function, we base the following example on the specific utility function belonging to you, the individual reader. First, an estimate of your net wealth is required: the total of all your assets less existing liabilities. Because its value is certain at the present moment, it should be entered in the first row of Table 4.1 under the column Certainty Equivalent. Now we offer you an investment in retailing umbrellas on New York City street corners. If it rains, you will double your wealth. If it is fine, the umbrellas may be returned Table 4.1 Utility Function Derivation Case

Optimistic

Pessimistic

Net Wealth Umbrella Investment Robbery Taxation

Certainty Equivalent $

$ =2W $ |$

$

0

=W |= 1.5 W

=W

|S

| = 0.5 W

$ $ $

% of Wealth 100

100


to the supplier at no loss. What is the maximum nonrefundable participation fee you would be willing to pay in order to share in this marketing venture if the probability of rain is 50% ? Again, complete Table 4.1, placing the figure for double your wealth in the column designated Optimistic and your maximum participation fee plus your current wealth under the Certainty Equivalent column. Suppose, instead, we consider the risk of robbery or fraud, which would reduce your current wealth to zero. If the probability of theft is 50%, what is the maximum one-time insurance premium you would be prepared to pay to cover you against that loss? Subtract this premium from your current wealth, and place the result in the Certainty Equivalent column. Finally, consider the case of two taxation proposals under consideration by the federal government. Proposal 1 would lead to a reduction in the value of your current wealth of 50%, while Proposal 2 would increase it by 50%. If you believe that the proposals are equally likely to be adopted, how much, if anything, would you be prepared to pay to ensure that the whole scheme is dropped by the government? Subtract this payment from your current wealth and enter the result in the final Certainty Equivalent slot. Likewise enter the dollar values of the optimistic and pessimistic outcomes. Now complete the final column in Table 4.1 by computing each certainty equivalent as a percentage of initial wealth. Your utility function may then be plotted on chart paper. Take first the umbrella investment, and locate your figure for the certainty equivalent as a percentage of wealth on the horizontal axis. The first point on your utility function then lies at the intersection between a vertical line from this wealth level and the dotted line from 150 on the utility index axis. Similarly plot the intersection between your certainty equivalent as a percentage of wealth under Robbery and the utility index of 50. Finally, plot the intersection with utility index 100 and the Taxation case. Starting at the origin, fit a smooth curve through these points. Compare the result with the logarithmic utility function graphed in Figure 4.5. How does your degree of risk aversion differ? Examine your risk discount in each case, given that the expected values are 150% in the case of umbrellas, 50% for robbery, and 100% for taxation. Now apply this certainty equivalent method to the valuation of a share.32 Recall the dividend valuation model used in Section 4.1:

We are now able to acknowledge explicitly that the dividends in each future period are uncertain, depending on the performance of the company, its opportunities for new investment, financing decisions, and so on. If we could estimate the range of possible dividend outcomes, the probabilities associated with each, and the investor's utility function, we could calculate the certainty equivalent of the dividend possibilities in each period, giving:

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Since we have already converted the relevant cash flows (numerator) to dollar certainty equivalents, the relevant comparison must be with a "default-free" asset. For this purpose it is customary to use U.S. government bonds that have a certain nominal dollar return if held to maturity.33 Hence the "required" rate of return r used to discount the certainty equivalents of future dividends will be the yield on such a default-free asset. The process of valuing a share would have us 1. 2. 3. 4.

Estimate a range of dividend outcomes for each period Attach a probability to each outcome Compute the certainty equivalent for each period Discount these CEs back to present value at the risk free rate

From a theoretical standpoint, this is the correct method of pricing a stock. In practice, it presents a number of significant problems. The first is clearly the specification of the individual's utility function. Of course we could go through a more detailed version of the process used to construct Table 4.1, but doing so is clearly cumbersome. It also prevents us from developing any more general method of share valuation that might be independent of the individual's utility function. Researchers have therefore searched for a workable mathematical approximation. One of the earliest suggestions was made by the Swiss mathematician Bernoulli (1730), who proposed a logarithmic specification corresponding to the solid curve in Figure 4.4: U(W) = alogW+b, where U(W) is the utility of wealth and W is the dollar value of an individual's net assets. Perhaps there were some similarities to your actual utility function charted from Table 4.1; if not, don't worry: Logarithmic utility is merely a convenient example. The Bernoulli utility function exhibits risk aversion due to diminishing marginal utility of wealth because the slope becomes smaller as wealth increases. Since log(l) = 0, the-curve intersects the horizontal axis at some point to the right of zero determined by the value of b, but it cannot intersect the vertical axis. At the same time, the log function has some questionable properties as a representation of utility. As wealth approaches zero, for instance, it implies that utility approaches negative infinity. Moreover, log functions display what is called "constant relative risk aversion." This term refers to the ratio of an individual's risk discount (as defined earlier) to his or her wealth being constant for any level of wealth. It seems more plausible, however, that as individuals become wealthier they also become less risk-averse. One major alternative class of functions suitable for the representation of utility are quadratics, where U(W) = a + bW + cW2. Such a function demonstrates both increasing utility with higher wealth and risk aversion when the coefficients are such that b is positive and c is negative. While retaining these basic proper-

102


ties, it has the advantage of more flexibility than the log function in the sense that its specific slope is quite malleable, allowing it to fit the substantial variety of risk aversion profiles we might expect to observe in practice. It has an important flaw, however: The quadratic function implies that individuals have increasing relative risk aversion: That is, an individual's risk discount as a percentage of wealth increases as wealth increases. This is a doubtful proposition in practice. We cannot avoid the conclusion, therefore, that the specification of utility presents a significant difficulty in implementation of the certainty equivalent approach. The second obstacle to practical implementation is simply that the process of calculating the certainty equivalent is cumbersome: The number of possible outcomes is likely to be large, requiring an equally large number of probability estimates. Fortunately, the whole process can be considerably simplified, albeit at the expense of some practical, but not always fully justified, assumptions. Specifically, if investors are assumed to have quadratic utility functions or if the probability distribution of returns is assumed to approximate the "normal" (Gaussian) distribution, then all of the relevant information about risk and return can be summarized into two measures: the expected value (equivalent to the mean) and the variance of the distribution of returns. In that case, by estimating the mean and variance associated with returns on a security directly, we can avoid the cumbersome process of listing all possible returns and their respective probabilities. The advantages are obvious, but just how onerous are the necessary assumptions? The assumption of quadratic utility has some acceptable features, but as already noted its usefulness is limited by the implication of increasing relative risk aversion. The validity of the alternative—namely, that the returns on securities are normally distributed—is essentially an empirical issue. A number of researchers have examined the question, concluding that while the actual distribution tends to display the bell-shaped form of the Gaussian curve, there appear to be too many large positive or negative values and there may also be too many values near the mean.34 Nevertheless, the use of mean-variance analysis remains a worthwhile approach to the demand for securities and ultimately their valuation. The reason is simply that a more realistic approach does not yet exist. Accepting the premises of the conventional approach, the next step is to develop a method by which direct estimates of the mean and variance of returns on securities can be obtained (see Section 4.2.4). Before proceeding, we recall that returns are the sum of dividends and price changes. Since dividends evolve fairly smoothly over time, the distribution of returns is effectively determined by the distribution of price changes. The actual distribution of day-to-day changes in the Standard & Poor 500 index over the years 1969 through 1990 is shown in Figure 4.6.35 The most conspicuous feature of Figure 4.6 is its asymmetry; that is, there

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103

Figure 4.6 The distribution of daily changes in the S&P500 stock index. Note: Except for those at the extreme left and right, each of the fourteen bars corresponds to an interval with a width of one-half of the standard deviation; the mean itself is located between the seventh and eighth bars. The bars at the extreme left and right correspond to open-ended intervals more than 3 standard deviations away from the mean. The mean was about 0.02% per day, equivalent to an average increase of about 5% per year, and the standard deviation was a little less than 1% per day. The length of each bar is proportional to the number of cases in the corresponding interval; thus there were 1,379 days in the tallest bar (out of a total of 5,558 days) and about 25 in each of the shortest bars.

are more small price increases (relative to the mean, which is also positive) than there are small price decreases. This skewness is confirmed by the third momen around the mean, which is negative. Less visible but more important is the rela tive abundance of large positive and negative price changes compared to the normal distribution. According to tables of the normal distribution there shoulc be about seven cases in each of the "tails" (the extreme left-hand and right-ham bars); actually there are more than three times as many. The distribution of stock price changes is therefore "fat-tailed," meaning that calculations of risk based 01 the normal distribution may be misleading. The same phenomenon has been observed in other financial instruments, particularly futures contracts. 4.2.4 Estimating the Mean and Variance of Returns The first method of estimation that might be considered is simply to compute the mean and variance of the actual returns on a stock over its past history. Thus the return in any year, quarter, and so on, may be computed as:

104


where divt is the dividend paid during the period and P t+l and Pt are the prices of the share at the end and beginning of the period, respectively. The sample mean is then simply

where n is the number of periods in the sample, and the sample variance is

This approach may provide a useful starting point for the analysis. Indeed, in the case of the variance it may be the best estimate we have available to us in practice. Looking to the past, however, does ignore the basic fact that the mean and variance of a stock's return will depend on the performance of the firm in the markets of the future, in the face of competition, technological change, and shifts in the demand for its products over coming years. Past performance will be a poor guide if the markets in which it operates change fundamentally. Thus, if we have any information at all about the likely future competitiveness and growth or decline of the firm whose stock we are valuing, we should attempt to explicitly incorporate that into our estimation of the mean and variance of its future returns. In fact, this is primarily what the large research staffs retained by many of the leading stockbrokers and mutual funds aim to do. They take information on past performance obtained from the annual reports of individual companies and various other sources of data and they comment on trends in supply, demand, and competition within that firm's markets. Drawing on specialist knowledge gained by observing an industry over a long period, they produce forecasts of the mean or "expected" earnings for a number of periods in the future. This important topic of fundamental analysis (so termed because it attempts to use data on likely future earnings to derive a "fundamental" value of the stock, which may differ from its current market value) is discussed in Chapter 7. 4.2.5 Conditional Probabilities and Expected Values

We now introduce an important refinement of the concepts of probability and expected value (this will be used again in Chapter 5). Suppose you own some bonds in the PQR corporation, which has just reported a large loss. Given this loss you would like to know the probability that PQR will default on its bonds within a certain period, say 1 year from now. This probability may be written

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105

Prob (D|L), Where D represents default on the bonds and L the known loss. This is a conditional probability with L as the condition under which the probability of the outcome D is to be evaluated. We are not now concerned with the actual evaluation of Prob(D||L), only with the concept. To take another example, let it be known that the stock market went up today, a fact we shall denote by Ut. What is the probability of the outcome U t + l , which means that the market will also rise tomorrow? The latter probability may be expressed as Prob(Ut+1|Ut). Conditional expected values are defined similarly. For instance, if dpt is today's change in some stock market index and dpt+1 is tomorrow's change, then EV(dp t+1|dp,) is the conditional expected value of tomorrow's change given today's change. As we will see in Chapter 5, this conditional expected value plays a key role in defining market efficiency. The expression appearing after the vertical bar in the preceding formulas may involve more than one condition. Thus EV(dp t+1\dpt-1,dpt) represents the expected value of tomorrow's price change conditional not only on today's but also on yesterday's price change. Clearly this idea can be extended to any number of conditions.

4.3 THE PORTFOLIO COMPLICATION

The more sophisticated analyses of demand for goods and services examine the problem of consumer choice not in terms of demand for a good per se but as a combined set of demands for the individual attributes it embodies. Choosing a particular wine, for example, is actually the choice of the bottling that offers the combination of color, bouquet, taste, alcohol content, and so on that most closely approximates the exact mix of these attributes the purchaser desires. The extent to which the mix of attributes embodied in a particular bottling or brand matches the buyer's "ideal" bundle of attributes, in turn, has important implications for the shape of its demand curve. Specifically, the better the match, the higher the relative price the purchaser is prepared to pay before he or she will be induced to shift to an alternative brand. This analysis applies equally to the investor's choice between the many securities offered in the market. It is unlikely that any security alone will have the exact mix of attributes that the investor desires. He or she will therefore demand the security that appears to come closest to this ideal. (We say "appears" because the "labeling" on securities is often more difficult to decipher and interpret than that on wine!) In addition, investors have the possibility of mixing different securities together in the form of a portfolio in order to come closer to their desired bundle of attributes. The first task in analyzing the demand for securities is therefore to define the relevant attributes involved. Suppose you have a portfolio of securities, the overall return on which fluctuates over successive business cycles. You are then offered the chance to

106


purchase an additional security that, while very volatile in terms of its returns overall, tends to fluctuate countercyclically. It should be obvious that by adding this countercyclical security to the portfolio, the overall return can be stabilized. Even if that security viewed in isolation is highly risky, it would be strongly favored by a risk averter as part of a portfolio due to its stabilizing influence. Although this is an extreme example, it illustrates the more general point that the true measure of a security's risk is not its own variance but the amount of additional volatility introduced into an investor's portfolio by including it. This condition leads us to an important distinction between systematic and unsystematic risk.37 That part of the volatility in a security's return that is positively correlated with the other securities in the portfolio will serve to exacerbate the fluctuations in the overall return on the portfolio. This "correlated" element is known as systematic risk. That part of a security's return volatility that is independent of fluctuations in the return on other securities in the portfolio will tend to "wash out" as we put a large number of securities together. In other words, this uncorrelated or unsystematic portion of a security's volatility can be diversified away by spreading one's investment over a large portfolio of securities. Our conclusion, therefore, is that the critical measure of mean and variance from the investor's standpoint are those of the portfolio. To understand the variance of a portfolio, in turn, we must examine the split between systematic and unsystematic risk, hence the correlations between returns on different securities over different states of the world. In order to gain an appreciation of these relationships, we begin with the two security case. Using the techniques discussed in Section 4.2.4, suppose we have computed expected returns for each of the two stocks (ERl and ER2) for our relevant investment horizon, and that past experience has provided us with estimates of the variance of the returns on each (var1 and var2). By examining past returns we can also estimate the correlation between the returns on the two stocks (p12) as follows. First we take the actual returns on the two stocks for various periods: R11 . . . Rlt . . . Rln R21 • • • R2t • • • R2n R

where t=l, . . . ,n, and compute the meansR*1and R*2. The covariance between return on the two stocks is then:

This statistic is then usually scaled to between -1 and +1 for ease of interpretation by computing the correlation coefficient:


107

A value of 1 indicates that fluctuations in returns are perfectly synchronized, while a value of — 1 indicates exactly opposite movements, and a value of zero, that the fluctuations in returns on two stocks are independent of each other. From these basic statistics the mean and variance of different portfolio combinations can be computed. If the proportion of our total investment in security 1 is a fraction denoted a, then the remaining fraction (1—a) is the proportion invested in security 2.38 The expected return on the portfolio is then

The variance of the portfolio is given by:

where l and 2 are the standard deviations of returns on the two individual securities. The most interesting aspect of this formula is the way the variance of the portfolio as a whole changes with the degree of correlation between fluctuations in the returns on each security, as measured by the correlation coefficient p12. Let us look more closely at the third term on the right in the equation, namely: 2a(l — a)p12 . Notice that, when the two standard deviations are given, the smaller pl2 becomes, the smaller is this component of the portfolio variance so that the overall varpf declines. When the returns on the two securities fluctuate completely independently of each other, this third term disappears altogether, causing varpf to decline still further. Obviously a negative correlation could reduce varpf even below this level. This formula expresses what we described earlier as the benefits of portfolio diversification. These benefits accrue even when we have only two securities from which to chose provided that movements in their returns are not perfectly positively correlated. We can illustrate with a simple numerical example. Suppose the expected return on security 1 Rl = 10% with a standard deviation of =4%, and similarly R2 = 20% and 2 = 7%, and we mix the two on a 50:50 basis. Computing pf for different possible values of the correlation coefficient p12 gives the values shown in Table 4.2. In each case a 50:50 portfolio has the following expected return: Rp = (0.5*10) + (0.5*20)= 15%. Table 4.2 p12 p/

Correlation vs. Portfolio Standard Deviation

1.0

0.5

0.0

5.5

4.82

4.03

-0.5 3.04

-1.0 1.5

108


What does this analysis imply about the risk-return trade-off? If we computed Rpf and pf for different portfolio mixes along the spectrum from investment of our entire portfolio in the low-risk security 1, through the 50:50 split, to the other extreme of placing our entire investment in the higher risk, higher return security 2 we would come up with a risk-return trade-off. The shape of this trade-off would differ depending on the degree of correlation p12 between returns on the two securities. The resulting trade-offs for five sample levels of correlation are shown in Figure 4.7. Notice that as the correlation between returns on our sample stocks declines from its maximum of 1, we have the opportunity of ever lower risk for any given level of expected return provided we mix the two securities so as to take advantage of the benefits of diversification. In the extreme case of two securities that are perfectly negatively correlated, it is possible to eliminate the volatility of return on the portfolio altogether by choosing the appropriate combination. It is a relatively straightforward matter to go beyond two securities and generalize the model to any number of stocks. For some total number of stocks available in the market, call it n, the formulas for a portfolio's expected return, variance and standard deviation, become:

where a, is the proportion of an individual security i in the portfolio. Testing different portfolio mixes (different sets of ai), we can then generate

Figure 4.7

Risk return trade-offs for different levels of correlation


109

an opportunity set of available portfolio risk-return combinations. Any such combination is "inefficient" if there exists a better portfolio combination (i.e., one that either offers higher return for the same level of risk or a lower risk for the same return). These inefficient portfolios fail to exploit the potential for diversifying away unsystematic risk and will not be selected by an astute investor. After eliminating the inefficient portfolios, the investor is left with the "efficient" ones, all of which can be optimal for some desired combination of risk and return. The actual choice among the efficient portfolios depends on the risk-return preferences of this particular investor.39 Once the desired risk-return combination is decided upon, the portfolio structure (i.e., the proportions invested in individual securities) is then determined by optimal diversification alone. This result serves to reemphasise the point made earlier that, given the importance of the correlation between returns on securities in determining the real level of risk associated with an individual stock, the decision of how much of a particular security to buy is unavoidably part of a wider portfolio choice. It cannot be viewed in isolation from an individual's other investments. Finally, a word of caution is in order. Although diversification is a powerful device for achieving a desired risk-return combination, it is not always optimal. Consider the case of a small businessman who enjoys an annual return of 20% on the capital invested in his firm, but with a high variance . The alternative investments available to him in the market all have returns well below 10%, though most of them have much lower variances than and some of them even have negative covariances with his business income. By investing in some of these alternatives he could certainly reduce the variance of his portfolio, but his return would also be much smaller. Consequently, he may decide not to diversify and to be content with his high return despite its large volatility. This decision would be all the more compelling if credit for his firm is difficult to obtain or very expensive, in which case he could not withdraw money from the firm without endangering its viability. Diversification, in fact, is common but by no means universal in the management of capital. It is distinctly uncommon in other important markets, particularly the labor market. Some people invest considerable time and money to become doctors or lawyers. These occupations are not riskfree, yet it is rare for someone to qualify herself or himself for a second occupation just in case the chosen one does not work out. The small-business example just discussed is actually on the borderline between the capital market and the labor market because going into small business is tantamount to choosing an occupation. The idea of diversification embodies the popular wisdom of "not putting all your eggs in one basket," but sometimes it is better to "put all your eggs in one basket and watch that basket."

5 Securities Markets and Their Efficiency

Imagine a situation where shares are sold in much the same way as used cars, with prices set through a haphazard system of bargaining between individual buyers and sellers, and with information about the different items on offer transmitted through a variety of channels from "for sale" or "wanted" notices to newspaper advertisements or dealer displays. Under such a regime, reliable and reasonably precise information about the value of your shares would be very difficult to obtain. The cost of searching for a potential trading partner with a matching desire to sell or buy a particular stock would in many cases make trading prohibitively expensive,1 as would the cost of verifying that the seller had a valid title to the stock being delivered and that the buyer has the funds with which to pay. We are so used to the existence of organized exchanges, where millions of securities change hands every hour, that it is easy to take for granted their contribution to the ease with which securities can be traded. The discussion in this chapter therefore begins with an analysis of the economics of securities trading and the rationale for brokers and central trading places. In the following section we take a closer look at the types of orders buyers or sellers may place in the market and the way these are executed. This topic leads to a discussion of the system of "specialists" commonly found on the stock exchanges designed to provide a smooth and continuous market for individual stocks. Having outlined the mechanics of securities trading in some detail, we proceed to examine the implications of central exchanges where information flows rapidly between participants for the efficiency of the stock market as a whole and, in particular, the "random walk" behavior of share prices. 110

CENTRAL TRADING PLACES

11 I

5.1 CENTRAL TRADING PLACES

Some of the problems that would arise if stocks and bonds were traded in the same way as assets such as used cars have already been alluded to. The first important steps toward removing those impediments is the interposition of brokers as intermediaries between potential buyers and sellers. The role of the broker is basically to collect information about supply (specifically, the characteristics of the goods being offered, quantities, prices asked, and the integrity of those desiring to sell) and corresponding information about demand from those wishing to buy. The broker has lower costs than any individual buyer or seller because he or she can spread fixed search costs over a large number of transactions. In addition, the broker benefits from accumulated experience of how and where to obtain reliable information. Some of these economic benefits are absorbed in the broker's profits, while the remainder are passed on to customers in the form of better information and lower transactions costs.2 The market for real estate is a classic example where brokers trade on the benefits just described. The fact that there are many independent real estate agents in most areas means that transactions costs may be higher than they could be, since search costs are duplicated by individual agents collecting essentially the same information simultaneously; the offsetting advantage, of course, is competition among brokers. The efficiency of the market can be improved by an exchange of information among brokers, as occurs in a multiple listing network. It is this elimination of duplicated search costs that also underlies the use of a central trading place, where buyers and sellers (or the brokers who represent them) get together, exchange information about supply and demand (mostly by making bids and offers), and execute trades. In the form of open-air markets such trading places exist in many parts of the world, though they have become rare in the United States. In this book we are mostly concerned with centralized trading places in financial instruments, particularly stocks, options, and futures contracts; the latter two markets are discussed in Chapters 8 and 9, respectively. 5.1.1 Stock Exchanges

Like the real-estate market, the market in corporate securities is mostly a market in existing assets.3 In addition, both facilitate the creation of new assets, such as newly built houses and newly issued shares. Trading in existing assets is economically important because investors would be hesitant to acquire assets if they could not sell them when they wanted to. By providing liquidity and price information, markets in existing assets encourage the purchase of newly created assets. Unlike houses, corporate securities are sufficiently homogeneous to permit a highly organized form of trading. The physical gathering of those interested in trading securities under the now famous buttonwood tree on the Wall Street of 1790 was the origins of the

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SECURITIES MARKETS AND THEIR EFFICIENCY

New York Stock Exchange (NYSE).4 New York weather can be credited with its move indoors to the Tontine Cafe in 1793. Subsequently it erected buildings of its own, including the present one near the corner of Wall and Broad Streets. The move indoors made it easier to enforce agreements on standard trading times, rules of conduct, brokerage charges, and exclusivity so that trading would only take place between members. These conditions were formalized in 1817 with the NYSE's first constitution. The institution of exclusivity arrangements has three advantages. First, it further reduces the costs of trading because the integrity (solvency and reliability in delivering on agreed trades) of the other party is ensured by membership of the exchange and hence does not need to be checked every time a trade is about to take place. Second, it allows for certain uniform rules to be agreed upon and universally adhered to. These rules mean that many of the details of the trade (such as the definition of lot sizes, delivery terms, etc.) are effectively determined by standard practice. Thus, most of the information that would normally have to be exchanged in the course of a trade is simply "understood" each time a price is quoted; as a result, transaction costs are reduced drastically. Third, it allows the exchange to invest in its own physical assets (such as buildings and quotation equipment) and operate with its own staff by levying various fees on members.5 From the public's point of view, however, exclusivity had an important disadvantage: It facilitated the fixing of standard fees by brokers. In fact, this anticompetitive practice became institutionalized in the NYSE rules (and those of most other exchanges) and prevailed in the United States until it was outlawed by legislation in 1975. At present, commissions (another name for brokerage charges) can be negotiated between investors and their brokers. Many "discount brokers" offer execution of orders at much lower fees than the "old-line" houses, which also provide their customers with advice and research. Today the NYSE has 1,366 active members, a maximum that has remained constant since 1953 despite an enormous increase in the volume of trading.6 Memberships are valuable because they give trading privileges and because they imply a share in the assets of the exchange, but these advantages are to some extent offset by the periodic dues that members have to pay. Large firms often find it convenient to own more than one membership; at the end of 1991, in fact, there were only 518 different firms owning memberships. To become a member, certain financial and personal criteria set by the exchange must first be satisfied. Then a membership or "seat" has to be purchased from a present member. The market in which memberships are traded is known as the seat market (which does not mean that a busy stock exchange provides many opportunities for sitting down). Since exchanges are rarely liquidated, the price of a seat depends on the income that can be expected from exercising the trading rights that go with it. In the short run, fluctuations in seat prices reflect fluctuations in trading volume, but in the longer run, changes in competitive conditions—such as the introduction of negotiable commissions—may also be


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important. In April 1987, the price of an NYSE seat reached the million-dollar mark for the first time, but it has remained well below that level since "Black Monday." The value of a membership, incidentally, also serves as collateral against any claims the exchange may have on its members. There are four main types of membership. Floor brokers execute orders for their individual customers or their member firms (such as Merrill Lynch or E. F. Hutton). There are also floor brokers, known as "two-dollar brokers," who are not associated with a large member firm; they accept orders from other brokers who are overloaded in peak periods (or may not wish to be identified) and execute them for a flat fee. Floor traders, by contrast, buy or sell only against their own portfolio rather than on behalf of either a customer or another broker. Essentially, they are speculators seeking to profit from their instant access to market information by virtue of being on the trading floor, along with the fact that they avoid paying commissions by acting directly for themselves. Often floor traders buy and sell a stock within the same day, seeking to profit from very short-term fluctuations in supply and demand, an activity known as day trading. Specialists constitute a category of members characteristic of U.S. stock exchanges. At present there are about 50 specialist firms on the NYSE, each with several members. Each is charged with maintaining an orderly market in a number of stocks (those in which it "specializes") that have been assigned to the firm by the exchange. A specialist acts both as a brokers' broker (executing trades for floor brokers) and as a dealer (buying and selling on his own accounts and at his own risk). When buy orders temporarily exceed sell orders, the specialist is expected to sell stock from his inventory (which may be negative) in order to equalize supply and demand. Conversely, he is expected to even out excess supply by purchasing stock for his own portfolio. In this way the specialist helps to achieve an orderly and continuously liquid market. Another important responsibility of the specialist is to handle "limit" and "stop" orders left with him by floor brokers, the mechanics of which are discussed in the next section. (See also Section 5.1.3 for more details about the operations of specialists.) "Off-floor" members, unlike the three categories just mentioned, do not engage in appreciable activity on the exchange floor. They rely mostly on floor brokers for their transactions, but their membership gives them the option to do their own executions if it is to their advantage. The prestige conveyed by membership may be valuable to broker firms in dealing with investors, and it gives them a voice in exchange decision making. In addition to the rules of conduct placed on members, exchanges also place requirements on the companies whose shares they trade. 1. To qualify for listing on the NYSE, the company must exceed a minimum size. Specifically, it must have at least 1 million shares outstanding with a market value (sometimes estimated on the basis of net tangible assets) in excess of $16 million, and there must be at least 2,000 holders

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2. 3. 4. 5.

with 100 shares or more. This criterion excludes the vast majority of the millions of corporations that exist in the United States. It must have demonstrated past earning power of at least $2.5 million profit before taxes during the past year and $2 million for each of the 2 years before that. It must agree to NYSE reporting standards, including the publication of its earnings each quarter. The company must maintain a share registrar and transfer agent in New York City.7 A majority of the company's directors must vote in favor of listing. This requirement means that an otherwise eligible corporation may choose to remain unlisted, thus ensuring that it will stay under private control.

Firms that are unable or unwilling to be listed on the NYSE can apply for listing on the American Stock Exchange (also located in New York), on one or more of the regional exchanges (such as those in Boston, Chicago, Los Angeles-San Francisco, and Philadelphia-Baltimore-Washington), or in the overthe-counter (OTC) market (see Section 5.2.1). The regional exchanges generally have less stringent listing requirements than the NYSE and therefore appeal to smaller companies. Large corporations are often listed on several exchanges, and most of the trading on the regional exchanges is now in securities that are also listed on the NYSE. An electronic network known as ITS (Intermarket Trading System) links the exchanges and makes it possible for orders to be executed on the exchange where the price is most favorable to the buyer or seller. Tables 5.1 and 5.2 present information on the relative importance of the various U.S. stock exchanges in recent years; to add further perspective, the over-the-counter market (or at least that part coordinated by the National Association of Securities Dealers Automated Quotations, or NASDAQ) is also included. Looking first at exchange trading, we see that the NYSE has remained dominant during the period covered, with a 1992 market share of 81% in volume and 86% in value, compared to 80% and 84%, respectively, in 1980.8 The regional stock exchanges have by and large held their own by these criteria. The big loser, at least in relative terms, has been the American Stock Exchange, whose share in volume declined from 11% in 1980 to 5% in 1992. A different picture emerges when the over-the-counter market is considered. That market increased its share of total trading considerably; between 1980 and 1992 the volume share increased markedly and the value share rose even more. As a result, the NYSE handled only 43% of the total volume and 52% of the total value in 1992. The NYSE continues to be the first in equity trading, but its position is increasingly threatened by the OTC market, whose organization, as discussed in Section 5.2.1, is quite different. While not as overwhelming as it used to be, the preeminence of the NYSE may be attributed largely to the high market liquidity it provides. Small and


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Table 5.1

Annual Volume of Trading in Shares" (billions of shares)

Exchange

1980

1985

1990

1992

New York American Midwest* Pacific c Other regional

12.4 1.7 0.6 0.4 0.4

30.2 2.1 2.3 1.4 1.1

43.8 3.1 2.5 1.7 2.2

53.3 3.6 3.0 2.1 3.5

ALL EXCHANGES

15.5

37.0

53.3

65.5

6.7

20.7

33.4

48.5

22.2

57.7

86.7

113.0

NASDAQ TOTAL a

Including rights and warrants, but not options.

b

The Midwest Stock Exchange was recently merged into the Chicago Stock Exchange. Value figures are not available for the (pre-merger) Chicago exchange, which is included in "other regional." c

Los Angeles-San Francisco.

Source: 1994 Statistical Abstract of the United States, tables 812 and 816. Table 5.2

Annual Market Value of Trading in Sharesa (billions of dollars)

Exchange

1980

1985

1990

1992

New York American Midwestb Pacific c Other regional

398 35 21 11 11

1023

1390

1757

26 79 37 35

36 74 45 84

42 87 58 89

ALL EXCHANGES

476

1200

1612

2033

69

234

452

1350

545

1434

2064

3383

NASDAQ TOTAL a

Including rights and warrants, but not options.

b

The Midwest Stock Exchange was recently merged into the Chicago Stock Exchange. Value figures are not available for the (pre-merger) Chicago exchange, which is included in "other regional."

c

Los Angeles-San Francisco.

Source: 1994 Statistical Abstract of the United States, tables 812 and 816.

medium-sized orders—say of 1 up to 100 round lots—are normally executed instantaneously without any appreciable effect on the prevailing price. Even very large orders, sometimes involving many millions of shares, can usually be executed promptly and smoothly as well.9 Extensive use of computers has enabled

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the exchange to keep pace with trading volumes that frequently exceed 200 million shares in one day. The largest volume to date occurred on the Tuesday (October 20, 1987) after "Black Monday" and exceeded 600 million shares; even this volume was handled without excessive delays. The bottom lines of Tables 5.1 and 5.2 highlight the tremendous growth of share trading in recent decades. Between 1980 and 1992, the number of shares traded multiplied nearly fivefold and their value increased more than sixfold.10 To some extent this increase was a result of more shares being listed due to new issues and splits; thus the total number of shares listed on the NYSE went up from 22 billion in 1975 to 80 billion in 1989. In addition, shares have tended to turn over more frequently, most likely as a consequence of lower commission rates; the "turnover ratio" (shares traded as a percentage of shares listed) rose from 21 in 1975 to 52 in 1989. 5.1.2 Types of Orders and Their Execution

The simplest type of order is the market order: a request to the broker to buy or sell as soon as possible at the best price then obtainable on the trading floor (i.e., at the "market price").11 Market orders have the advantage of rapid execution, which may be important in a fast-moving market. On the other hand, the "best price" is uncertain and may turn out to be disappointing, particularly in respect to an inactive stock, where it may reflect a short-term distortion or a wide spread between bid and ask prices. Sometimes the originator specifies that a market order is to be executed at a particular time rather than immediately. If the order is specified "market at close" (MOC) the execution price will be the closing price for the day. The major alternative is a limit order, which will only be executed at a price no worse than the limit: that is, no higher than the limit specified by the buyer or no lower than the limit specified by the seller. Its disadvantage arises in a rapidly moving market where the price may have passed the wrong side of the limit by a small margin when the order reaches the floor. In that case it will not be executed for the time being, causing the investor to "miss the market" by as little as 1/8 of a point (equivalent to 121/2 cents) per share. A different type of limit sell order serves to provide automatic protection against loss in the case of rapid price decline. It is known as a "stop-loss order" or, more generally, as a stop order. In this case the investor constrains his or her maximum loss by specifying a limit price at which a market order to sell will be executed once the stock price drops to that level. Suppose that IBM is trading around 66; then an order to "sell 100 IBM at 64 on stop" will be executed only if the price drops to 64, at which time it becomes a market sell order. A stop buy order may be placed by a potential buyer (for instance, one who has previously sold the stock short); the order becomes a market buy order when the price rises to the specified limit.12 Since limit orders (including stop orders) may not be executed immediately,


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it is important to specify the time period during which they will be in force. Limit orders may be day orders, which automatically expire if unexecuted at the end of the day, or open orders, which may be entered for a week or some other period, or good till canceled (GTC), which are valid for 6 months unless notice is received to terminate them beforehand. Yet another type is fill or kill (FOK), where the order is canceled if it cannot be executed immediately.13 Pricing on the NYSE and most other exchanges amounts to a continuous auction in which both buyers and sellers make bids and offers all the time. The highest price offered by a prospective purchaser at any point in time becomes the "bid price," and the lowest offered among the sellers at the same time is the "ask price," which together are reported as the "bid-ask quotation." For many stocks, particularly if trading is inactive, either the bid price or the ask price (or, more rarely, both) are set by the specialist, as discussed in the next section. When a broker receives an inquiry from a client considering the sale of IBM stock, for example, she will first ascertain the current bid-ask quotation in the market. Suppose these are 66 bid and 661/4 ask, the specialist being willing to buy at least 100 shares at 66 and sell 400 at a price of 661/4. On receiving this information, the investor decides to place a market order to sell 100 shares. The account broker then transmits this order to her firm's representative on the floor who goes to the "post" where IBM is traded and checks that the 66-661/4 quotation is still in force. As long as the quotation remains valid, the broker knows she need not sell for less than 66 because the specialist will buy at least 100 at that price. At the same time, it is clear that there is no point in asking more than 661/4 since there are already limit sell orders unexecuted at that price. There is a chance, however, that there will be a buyer at 661/8, with 1/8 or 121/2 cents per share being the smallest increment in which bidding occurs. The broker therefore calls out "100 at 61/8" (the 60 is understood) to the floor, inviting another broker with an order to buy at 661/8 to "take" the ask, in which case information would be exchanged and the trade completed. It may be, however, that the broker fails to get a "take" and so must call the next lowest ask: "100 at 6." The first response will take the deal, and this may come either from the specialist or from another floor broker at the IBM post with a limit order to buy at 66. In many cases this kind of calling auction will be unnecessary since the bid-ask spread will already be 1/8. If so, the broker might just as well go directly to the specialist and execute the trade. Following execution, the buyer usually has 5 business days to pay and the seller has the same time to transfer the actual certificate that is evidence of ownership of the shares.14 Two institutions have been set up to facilitate the latter process. The first is a centralized clearinghouse operated by the National Securities Clearing Corporation. A record of each transaction is transmitted to the clearinghouse, which updates the stock and cash accounts of each member broker, thereby netting out all cross transactions (e.g., avoiding certificates on the same stock flowing in both directions between two brokers over a short space

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of time). At the close of each day, the opposite sides of each trade are verified for consistency, each member's accounts are netted out, and the outstanding balances of cash and scrip certificates are settled. A second system operated by the Depository Trust Company (DTC) virtually eliminates the movement of paper certificates altogether. Members of the system deposit the certificates, which are credited to their accounts. Transfers are then made in the form of electronic debits and credits to these accounts, reflecting shifting claims against this "bank" of certificates held by the DTC. The processes we have described so far trace the path of an order once it becomes a "market order." For a limit order (including a stop order), however, this chain of events will follow only after the specified limit price has been "hit." When a limit order is initially placed with a brokerage firm, its floor broker (or a two-dollar broker) will take it to the specialist in the stock, who will then enter it into his or her "book," where all unexecuted orders are listed. If there are already other limit orders in the book at the same price, each will be executed on a FIFO (first in, first out) basis once the price is hit, until demand or supply at that price is exhausted. 5.1.3 Specialists and Market Clearing

Since orders to buy and sell stock arrive in a more or less random pattern over time, the market price will fluctuate up or down depending on whether successive orders offset or reinforce each other (i.e., on whether they are on opposite sides or on the same side of the market). These random fluctuations will occur even if there is no persistent pressure for the price to move in a particular direction. Consequently, floor traders could profit from an ability to distinguish between random short-term fluctuations and more fundamental movements in the price. If, for example, a floor trader felt that the price had fallen simply because a few large sell orders happened to arrive together, he15 would buy the stock and resell it shortly thereafter at a profit when some further orders to buy arrived, causing the market price to rise. If his assessment were wrong, however, and a disproportionate number of sell orders continued to come in because investors had reduced their opinion of the fundamental value of the stock, the trader would be forced to take a loss on resale. To the extent that such speculators can accurately identify random price fluctuations caused by the coincidental arrival of buy or sell orders, their operations will tend to stabilize the market because they buy as the price begins to fall and sell as it begins to rise. This kind of short-term speculation has been institutionalized on the stock exchanges in the form of the specialists mentioned earlier, though not to the exclusion of floor traders. Together, floor traders and specialists provide greater stability and continuity to the market. The specialist has a particular advantage in distinguishing between random fluctuation and price trend because all unexecuted limit orders are listed in his


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book, as are the MOC and other time-specific market orders mentioned earlier. The specialist, in effect, knows the short-run supply and demand curves for the stocks in which he specializes. The word "curve" should not be interpreted too literally, since the price usually varies in steps of 1/8 rather than continuously. As a result, there may not be any price at which supply and demand balance exactly; the specialist will take up the slack. A simple example serves to clarify the operation of a specialist's book in the absence of trading by the specialist himself and by floor traders. Suppose XYZ last traded at 11:00 A.M. at a price of 91. After that trade, the specialist in XYZ has the following unfilled limit orders in his book: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Buy 1,000 at 88 or better Buy 200 at 881/2 or better Buy 100 at 89 or better Buy 500 at 90 or better Buy 200 at 903/4 or better Buy 300 at 93 on stop (i.e., buy at market if price rises to 93) Buy 100 at 931/4 on stop Sell 300 at 91 1/4 or better Sell 800 at 92 or better Sell 1,500 at 921/2or better Sell 200 at 89 on stop (i.e., sell at market if price falls to 89) Sell 200 at 87 on stop

The last market price lay between the lowest offer (91 1/4) and the highest bid (903/4)so that the book stands without further execution taking place. The stop orders are irrelevant for the time being because they will only be triggered when the current price changes. At 11:05 A.M. a market order to sell 1,000 shares of XYZ reaches the trading post. The specialist must then look for a price that will allow the market order to be executed in its entirety, while satisfying public limit orders first. If he were to set a price at 89, the book would provide total orders to buy of 800 (200 + 500 +100 for the three highest buy orders outstanding), not enough to fill the new order. At that price, moreover, order no. 11 (to sell 200 at 89 on stop) would be triggered so that excess supply would be 400: 200 remaining unsold from the new market order and a further 200 from the stop order. At a price of 88 1/2, order no. 2 (to buy 200 at that price) would also be activated, but this is still insufficient because of the extra supply from order no. 11. The price must therefore be reduced to 88, at which price 1,200 shares change hands. This will leave order no. 1 (to buy 1,000 at 88 or better) only 20% filled, so the bid will now be 88. This situation illustrates the point made earlier that with a discontinuously varying price it may not be possible to match supply and demand exactly. The lowest asking price on the specialist's book remains at 911/4(order no. 8).16 It will be noticed that the arrival of the new market order, in the absence of

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intervention by the specialist or by floor traders, causes the market price to drop from 91 to 88 in 5 minutes. This steep decline is due not only to the relatively large size of the new order but also to the triggering of stop order no. 11. Yet the arrival of the new order could be a purely random event without significance for the underlying value of XYZ stock. It is as if a plane suddenly hits an "air pocket" and drops several feet without deviating from its set course. It is in such circumstances that the specialist and the floor traders find their opportunity. Rather than allowing the price to be buffeted by a single market order, they may take a chance that buy orders will soon arrive to bring the price back to somewhere near its previous level. If this is their belief, they will take the opposite side of the new order, at a price well above the 88 that would emerge without their intervention. In doing so, of course, they assume a risk— namely, that additional market sell orders will arrive, forcing them take a loss on their expanded inventory. The reward for assuming this risk is that they can buy at the bid price and sell at the asking price, whereas outsiders have to buy at the asking price and sell at the bid price.17 The difference between floor traders and specialists is that the former can intervene at their discretion, while the latter have a definite responsibility for doing so. The specialists are charged by the exchange with maintaining a "fair and orderly" market in the stocks in which they specialize. Specialists, as we know, are also responsible for keeping the book of unexecuted orders, and this gives them a unique insight into the state of the market, particularly with respect to stop orders. In order to fulfill their assignments, each specialist firm is required to sell from its own inventory at the current asking price so as to smooth out temporary excess demand, and to buy on its own account at the current bid price when there is excess supply. This is called "leaning against the wind." Potential traders are thus assured that at any time there is a buyer and seller in the market (continuity), and that the bid-ask spread is kept close to its minimum of 1/8. Specialists are also required to execute all public limit orders they hold when the specified trigger price is hit, before buying or selling at that price for their own accounts. The specialists' obligation does not apply to orders above a certain size. Currently, specialists must stand ready to fill all orders up to about 1,100 shares. In the preceding example, the specialist would actually fill the new order (to sell 1,000 shares at the market) by buying at the bid price. Since the previous trade was assumed to be at 91, and the lowest offering (order no. 8) was at 91 1/4, the bid would probably be at 911/8.18By taking the other side of the new order at 907/8, the specialist would prevent the precipitous fall to 88 we found earlier. The specialist's own inventory can be a particularly useful buffer against unnecessary short-term price fluctuation when a block order (involving 10,000 shares or more) reaches the market. In this case, the specialist is required to execute all public limited orders until 1,000 shares, or 5% of the block if this is larger, have been absorbed. The remainder may be taken up by the specialist, at his discretion, into inventory; if so, the decline in the market price would be


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arrested. The enlarged inventory is then available for subsequent sales against upward fluctuations in the market, but if these do not materialize the specialist may have to sell at a loss (after executing all outstanding public orders in the relevant price range.) The specialist's inventory, incidentally, need not be positive; he may be short, and often is. Earlier we characterized exchange trading as a "continuous auction." Strictly speaking, this description is incorrect because the market is not open all the time; the NYSE, for instance, starts trading at 9:30 A.M. and closes at 4 P.M. (Monday through Friday).19 Trading in any particular stock, however, does not necessarily begin at 9:30. The first task of the specialist is to determine an opening price, which will reflect the buy and sell orders that have come in before the bell, the official signal that trading is permitted. In most cases, these orders are matched closely enough so that the specialist can quote an opening price at which all the market orders (and those limit and stop orders that are triggered at the opening price) are executed, perhaps with some help from the specialist's own inventory. The opening in that stock will then occur within a few minutes after the bell. Occasionally the preopening orders are very far from matching, for instance if there are many orders to sell and few to buy. The specialist may then be unable or unwilling to use his inventory to bring the orders into balance, and the opening is delayed. Efforts will then be made to find additional buyers (in this example) among large traders, probably at a much lower price than the previous close, until an opening price is found at which the market orders, along with the relevant limit and stop orders, can be filled. Such an "imbalance of orders" can also occur during the day, in which case trading in the stock is temporarily suspended. The exchange may also call for suspension if some important news item (for instance concerning a merger or acquisition) is pending. What all this amounts to is that the specialists' obligation to "make a market" is not absolute. The role of the specialists is controversial because they are both officially designated market makers and businesspeople aiming for profit. Despite close regulation by the exchange, the specialists' monopoly on important market information has often been criticized. It is argued that the substantial incomes of specialists are excessive for the service they perform, and that their economic function could be carried out more efficiently by an interactive computer system that kept track of limit orders. To the extent a specialist's market operations call for the exercise of judgment, however, it may be difficult to replace him or her with a computer.20 The future of the specialist system in the United States, and especially on the NYSE, will depend largely on its success in keeping the stock market reasonably stable. Occasionally there have been signs that the capacity of specialists to prevent excessive price fluctuations can be strained by a large volume of trading. As mentioned earlier, the stock markets as a whole weathered the "Black Monday" upheaval fairly well, but a few specialist firms were unable to cope and had to go out of business. A few other firms failed to meet the standards by

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which specialists are judged, causing the NYSE to reassign some of their stocks to other specialists. Even before "Black Monday," the phenomena of "program trading" and of the "triple witching hour" (to be discussed in Chapter 9) had caused concern. If these strains persist, the solution would not be to abolish the specialist system, which on the whole has worked well; it may be preferable to increase the number of specialist firms and to introduce more competition in the process by which stocks are assigned to them. The precipitous fall of stock prices in mid-October 1987 (including the three or four trading days preceding "Black Monday") puts the risks that specialists are expected to assume in a new perspective. During those few days, the overall price indexes lost about one-third of their value; some shares, of course, lost more than that. Is the obligation of specialists to "lean against the wind" reasonable, and indeed enforceable, in such conditions? If there were no potential buyers at anywhere near current prices, the specialists might be obliged to acquire stocks worth hundreds of billions of dollars.21 Even if they could get the necessary credit, the resulting losses in a declining market would soon wipe out their net worth. It might be tempting to conclude from this analysis that, if the specialists continued to perform according to the rules, they could not survive the kind of crash that occurred in 1987 (and also in 1929 and a few other years). This conclusion would be false: Specialists can protect themselves against catastrophic losses. More specifically, the introduction of stock index futures (to be discussed in Chapter 9) has made it possible for specialists and others to "hedge" their portfolios. How much use specialists make of this opportunity is a factual matter on which information is difficult to obtain.

5.2 FINANCIAL MARKETS WITHOUT CENTRAL TRADING PLACES

The stock exchanges, on which we have focused until now, are not the only important markets in financial instruments. The organization of the other markets in the United States differs significantly from that of the stock exchanges with their central trading places and specialist systems. A brief discussion of these other markets is useful not only because they are of great interest in themselves but also because it puts the special features of the stock exchanges in perspective. The bond market actually consists of several submarkets, particularly those in Treasuries, municipals, and corporate bonds; these securities were described in Chapter 3. None of them has a central trading place, and there are no specialists,22 though there are dealers who serve as market makers. The trading is conducted by telex and telephone. The organization of the bond markets, in fact, resembles that of the over-the-counter market in stocks discussed in Section 5.2.1.

FINANCIAL MARKETS WITHOUT CENTRAL TRADING PLACES

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The foreign currency market, like the bond market, has a very large volume but no central trading place and no specialists. Most of the trading is among banks; there are also brokers. The Federal Reserve intervenes occasionally, as do the central banks of other countries. It is a typical wholesale market in which the number of participants is relatively small—a few hundred at the most. Except for some large multinational corporations, firms engaged in international trade generally arrange their foreign exchange transactions through their bankers. Participation by the general public is strongly discouraged.23 The Federal Funds market, also discussed in Chapter 3, involves banks with occasional intervention by the Federal Reserve. There is no public participation. How can we explain this variety of organizational patterns? It would seem that there are two key factors: the number of participants and the number of different objects traded. Central trading places are economically justified when there are many participants, as is the case in equities, options, and futures; otherwise, the traders can communicate more cheaply by other means.24 This is why there is no central trading place in currencies; the case of bonds is less clear-cut. The number of traded objects is important in determining the viability of specialists as opposed to floor traders. The NYSE, for instance, lists more than 2,000 different shares, of which only a small fraction are actively traded during most or all of the trading hours. The specialists to whom those active equities are assigned can make handsome profits, but their economic function could arguably be performed more cheaply by floor traders or by multiple market makers competing with each other.25 Many other stocks, by contrast, trade several dozens of round lots per day at best. Specialists are most needed in those inactive stocks, since floor traders would not find it worth their while to watch them. In the absence of specialists, the market would be thin and prices would be erratic. On the futures exchanges, the number of different instruments (i.e., futures contracts) is much smaller; the presence of floor traders is usually enough to ensure reasonable continuity of prices. 5.2.1 The Over-the-Counter Stock Market

Despite the advantages described in Section 5.1.3, by no means are all shares traded on centralized exchanges. A large number of less important stocks (and some important ones) are traded on the over-the-counter market. This market has no central trading place; for many OTC stocks somewhat the same function is performed instead by an electronic communications network known as NASDAQ. While the OTC market is especially valuable for newly established corporations without the track record required for listing on a centralized exchange, we shall see in a moment that it has retained the allegiance of certain firms that have outgrown this limitation. The backbone of the OTC market consists of dealers who are willing to quote bid and ask prices for the stocks in which they "make a market," and who stand ready to execute at least one round lot at the quoted prices at any time.26

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The current quotations may be called up by brokers on terminals in their own trading room. The actual transactions, however, are made by direct negotiation between the dealer and the broker, and a different price may be agreed upon for a trade of more than 100 shares.27 As shown in Tables 5.1 and 5.2, the OTC market has gained ground on the centralized exchanges in recent years. It is perhaps more significant that such growth companies as Apple Computer, Intel, Lotus Development, MCI Communications, and Microsoft have continued their listing on NASDAQ even though they are sufficiently large and profitable to qualify for the New York Stock Exchange. In fact, the 1990 trading volume in MCI (a telephone company) on NASDAQ exceeded that of any company listed on the NYSE. It cannot be said, therefore, that the OTC market is confined to small companies hoping to grow enough to be listed on a centralized exchange. Indeed, the large volume in the five firms just mentioned suggests that the centralized exchanges no longer have much of an advantage over the less formal trading arrangements in the OTC market. The principal disadvantage of having multiple market makers is the possibility of conflicts of interest. Typically, the market makers on NASDAQ are stockbrokers who also deal with the public. They may be tempted to treat the positions of their customers as part of their trading inventories. As a result, the customers may not benefit from the best possible execution of their orders; sometimes selling customers, for instance, will simply receive an average price calculated at the end of the day rather than the highest bid price prevailing at the time they placed their order. Market-making brokers may also slant their investment advice to further their market-making activity. An investor in OTC equities would do well to inquire if his or her broker makes a market in the stock concerned. Prior to the abolition of fixed commissions on organized exchanges in 1975, a further market known as the "Third Market" began to grow as large institutions sought to avoid high brokerage fees by using a nonmember broker to search for another institution with a complementary supply or demand so that the trade could occur off the central exchange. More recently, it has become common for institutional investors to dispense with brokers and exchanges entirely and deal directly among themselves (these are known as "Fourth Market" trades). This trend has been facilitated by the establishment of computer networks that are capable of providing quotation and execution directly between buyer and seller: Instinet in the U.S.A. and Ariel in London. It appears that the third and fourth markets have not captured a large part of the trading in equities, but by providing alternatives to the stock exchanges they serve to keep the latter competitive. The basic economics of share trading, dominated by the benefits of eliminating the duplication of costly search and verification, still govern the organization of exchanges. Advances in computers and communications, however, are changing the technology by which those benefits are realized and apparently favor the OTC market. Ultimately, the result could be the replacement of central trading places with their electronic equivalent: a continuously updated, central database.28 However, the ability of the traditional exchanges and the OTC market to

STOCK EXCHANGES IN OTHER COUNTRIES

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cope with large volumes of trading and the lowering of brokerage charges has pushed that long-predicted development further and further into the future.

5.3 STOCK EXCHANGES IN OTHER COUNTRIES

In recent years, American investors, both institutional and individual, have increasingly recognized the potential gains from international diversification of their portfolios. Many brokers now trade for their customers 24 hours a day, following time zones around the globe. Thus they are paying increasing attention to stock markets abroad. These markets are also of interest because of the different methods of trading they follow. The relative volumes of equities traded on the world's major stock exchanges is shown in Figure 5.1. Although volume obviously varies from year to year, we can make a number of general observations. It is clear that the NYSE and NASDAQ together account for a very substantial part of the world trade in equities. In recent years, Tokyo has grown to become a very important market in global terms. London, although less than 40% the size of the NYSE in volume terms, has the largest activity in foreign (nondomestic) stocks. It is therefore one of the most important centers for investors who wish to trade an international portfolio of equities with the convenience of dealing on a single exchange. In the remainder of this section we concentrate on the London and Tokyo markets, explaining some of the major differences in trading practices and terminology between these exchanges and those in the United States.

Figure 5.1 Equity turnover on major stock exchanges ($ billion in 1990). Note: Frankfurt and Paris have approximately $10 billion and $5 billion turnover of foreign equities, respectively. Source: Data from the International Stock Exchange (London), Annual Report, 1992.

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5.3.1 The International Stock Exchange in London

The roots of the London Stock Exchange are to be found in the informal exchange of shares of various international trading ventures. As long ago as the late sixteenth century, when trade spread to newly discovered continents, the risks of individual voyages was increasing. Merchants sought to share the costs and potential revenues with other partners. But long periods at sea made it difficult to recruit investors without some means of selling the shares should the funds be required before the vessels returned and their cargoes were sold. Initially, this kind of trading was conducted in coffeehouses and other meeting places where entrepreneurs and investors met to raise the finance for such ventures. The formal stock exchange was constituted in 1802 to facilitate easy trading of shares and eliminate undue risk by establishing a set of recognized trading rules and a central trading place. Over the next 100 years there was an expansion in the types of enterprises whose shares were traded on the exchange to include industrial ventures and large-scale projects such as railways. The parties operating on the exchange also became more specialized, the most important distinction being between stockbrokers and "stockjobbers." Jobbers maintained stalls, known as "pitches," on the floor of the exchange. Without disclosing whether they were buying or selling, the stockbrokers would request prices for both transactions on behalf of their clients from a number of jobbers' pitches. The broker would then undertake the transaction with the jobber who offered the best price. Having quoted a price to a broker, the jobber was obliged to undertake the trade. The jobbers were thus dealers who took ownership of the shares, albeit often for only an instant. Like the OTC market makers in the United States, they made their profits from the difference between their buying and selling prices. Brokers, in contrast, were agents obliged to get the best price for their clients. They were compensated by fixed commissions. This system, called "single-capacity dealing" because the parties were either jobbers or brokers but could not act as both, operated on the London market from 1912 to 1986. Overnight on October 27, 1986, the London Stock Exchange underwent a major change in its trading rules, known colloquially as "Big Bang." Fixed commissions were abolished. The distinction between brokers and jobbers was dropped. Firms could now act in a "dual capacity," dealing in shares on their own behalf as market makers and also acting as brokers for their clients. In order to preserve integrity in performing two potentially conflicting roles, the new rules imposed certain restrictions. First, brokers were permitted to conduct business with their own jobber only when the in-house jobber at least matches the best price available elsewhere in the market. Second, all jobbers were required to continuously advertise their prices on the exchange's electronic price service Stock Exchange Automated Quotation (SEAQ), itself based on the NASDAQ system.


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Limits on corporate ownership of the new market makers were also lifted, allowing banks and other local and foreign financial institutions to operate directly on the London exchange. In the same year, the present International Stock Exchange of Great Britain and the Republic of Ireland was formed through the merger of the domestic stock exchange with international equity dealers operating in London. True to its name, Big Bang has initiated a great deal of change on the London market. The trading floor for shares has now disappeared.29 Unlike the system of matching buy and sell orders used on the NYSE (an "order-driven system"), London now relies solely on the display on screens of competing buy and sell quotes for the prices and quantities in which market makers undertake to deal (a "quote-driven system"). Trading in London now takes place by computer and telephone from brokers and market-maker's offices. Using the information displayed on the SEAQ screen, the investor chooses the best price available from a range of quotes and then arranges the trade with the most competitive market maker. The relative merits of quote-driven and order-driven systems have been hotly debated in London. One of the most important tests of the success of any securities trading system is how well it promotes market liquidity. As already mentioned, one important measure of liquidity is the bid-ask spread. An investor who purchased securities and then wished to sell them almost immediately would suffer a loss equal to the spread, even if the price of the security did not change. A large bid-ask spread indicates a less liquid market in the sense that investors cannot move between securities and cash at a low cost. Under London's quote-driven system, bid-ask spreads for most actively traded stocks narrowed somewhat after Big Bang to an average of about 1.75%, but the spreads for thinly traded shares have risen steeply to between 4% and 10% of the price of these stocks. Some people argue that the NYSE's order-driven system with "monopoly specialists" may be superior to a quote-driven system for thinly traded securities. They point out that a monopoly can reduce search costs; potential buyers and sellers know where to go to trade. When trades are only once or twice per week it takes time and effort to match buyers and sellers. This activity becomes more difficult the more market makers there are. They also point out that the specialist system may encourage the market maker to take larger positions in particular stocks, thus increasing the ability of the market to smooth out the price fluctuations that may result from a large buy or sell order in a market where transactions are few and far between. Opponents argue that the specialist system exposes investors to unnecessary risk of exploitation by these favored monopolists who have superior information by virtue of their privileged position. They have the full picture of the orders in the market, as well as unexecuted limit orders. Competition through alternative quotes, they argue, is the best way to minimize bid-offer spreads. This disagreement parallels the one about the role of NYSE specialists and about the relative merits of exchange trading and over-the-counter trading in the United States.

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Big Bang has also affected brokers' commissions. Following the abandonment of fixed rates, commissions for execution share trades declined from almost 0.5% of the transaction value before the reforms to a current average of 0.25%. Not surprisingly, the fall in commission rates was more than the average for large deals and actively traded shares as competition for this volume business intensified. Commission rates on small, retail trades have actually risen a little, toward 2%. The British banks and merchant banks, as well as major international companies like Merrill Lynch and Nomura (Japan's largest securities house), joined the market following Big Bang. In total, new entrants invested some $1.1 billion in former brokerage and jobbing firms. While a proportion of this money was paid to the existing partners, it also meant a large injection of capital, which market makers could draw upon to deal. Daily trading volume, although notoriously cyclical, has increased substantially, settling at almost double pre-Big Bang levels. Another significant change since 1986 has been the increased trading of nonBritish shares, which now takes place on the London exchange. At present there are more than 550 equities in foreign companies listed, including many of the major American, German, French, Italian, and Dutch companies. More than $200 billion (U.S.) of foreign equities are now traded in London each year—a much higher volume of international business than any other exchange in the world. Surveys have shown that up to half the turnover in large French and Italian companies and one quarter of all trading in major German shares takes place in London. In response, other European markets have begun to deregulate commissions and change some of their ancient trading practices. The Paris bourse staged its own version of Big Bang in 1990. The previously fragmented regional exchanges in Germany have come together to form a linked Federation of German Exchanges. A final aspect of the London Stock Exchange that differs from the NYSE (where transactions were normally settled within 5 days from the originating trade)30 is the use of an "account period." The trading year in London is divided into a series of "accounts" that are normally 10 working days, ending on a Monday. The account periods are defined by a first day of dealings, a last day of dealings, and an account day. Shares purchased during an account (i.e., between the first and last day of dealing, both included) do not have to be paid for until after the end of the account, on the account day, which is usually the second Monday after the last day of dealings. Nor, of course, does the seller of shares obtain the proceeds of sale during an account until the following account day. Prior to the end of an account, parties are simply sent a "contract note" advising them of the details of the bargain made on their behalf. There are also special provisions relating to shares purchased and resold during the same account. In this case, the trader does not actually have to pay for the shares at all but simply receives the net gain or pays the net loss on account day. Dealings within the same account do not attract the usual stamp


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duty of 0.5%. Moreover, the broker charges commission only once on the entire trade. It is also permissible to sell shares short during an account, so long as the same quantity is bought back before the end of the account. This alternative is of interest to traders who believe the price of a particular share will fall during the account period.31 5.3.2 The Tokyo Stock Exchange

Strong growth and heavy investment by Japanese corporations over the past 30 years have made the Tokyo Stock Exchange one of the world's most important securities markets. Several hundreds of millions of shares are now traded there each working day by both Japanese and foreign investors. In the boom before "Black Monday" in October 1987, Tokyo's most important stock index (the Nikkei 225, which covers the 225 largest Japanese corporate stocks) reached almost 28,000. These high share prices, combined with a strong yen, meant that the Tokyo exchange surpassed the NYSE as the world's largest exchange, as measured by the market capitalization of listed stocks. But the market proved volatile, and some years later, with share prices trading in a range 40% below this peak, Tokyo remains in the number two position. Since the end of World War II, the Tokyo Stock Exchange has operated as a private, nonprofit company subject to the Securities and Exchange Law administered by the Ministry of Finance. It has two types of members: regular members and Santoris. Regular members are companies whose main activity is to buy and sell shares on the floor of the exchange. They do so both as agents for their clients and for their own account. The main activity of Santoris, by contrast, is to act as intermediaries between regular members. In some ways they are like specialists on the NYSE: They have trading posts on the floor of the exchange from which they deal in specific securities. They differ, however, in the important sense that Santoris are not permitted to trade on their own accounts; they simply keep records of orders and act as agents of the regular members for a commission. A number of American and British broking firms currently hold regular membership of the Tokyo exchange. The marketplaces are divided between the "first trading section," comprising approximately the top 1,000 shares; the "second trading section," with around 400 shares of medium-sized companies and new issues; and the over-the-counter market, which handles trading of smaller "registered" and "subregistered" securities, as well as 95% of the trading in bonds. Dealing arrangements are unusually complex in that there are two types of trading and four types of settlement. The Itayose method, used primarily for bonds, treats all orders arriving before the opening of trading as simultaneous. Before any trades are consummated, all of these orders are examined in order to set an opening price that will clear both all market orders and all limit orders to the extent they can be matched. This matching process continues as new orders arrive. Under the Zaraba trading method, used for most shares, an opening price

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is first determined as just described. Then there is an open auction for all the outstanding orders that cannot be executed at the opening price, with new bids being made, and the lowest selling price bid and highest buying price bid being executed at any point in time in a sort of "double-sided" auction. Until 1985, this open auction system was conducted by floor traders through a mixture of frenetic hand signals and shouts, creating a scene much beloved by newspapers around the world as the image of dynamic capitalism. Part of this bustle arose because an estimated 70% of all orders on the Tokyo exchange are for less than 5,000 shares, so the ratio of orders to total trading volume is high. But now the bulk of transactions takes place by means of an electronic auction where the exchange's computers calculate the opening price and then register the subsequent bids. Only very large lot orders are still traded face-to-face on the floor and then entered into the electronic system. Once a bargain is struck, the most common form of settlement, termed a regular way transaction, is through the stock exchange clearing department on the third business day following the bargain. Business days in Japan include Saturdays, except for the third Saturday in each month. Other bargains may be made for settlement the same day (cash transactions) or at a fixed date within 14 days (special agreement transactions). This latter form of settlement is now rare. It dates from a time in the past where poor transport and communications in Japan necessitated a means of allowing time for people in remote locations to settle transactions. The final settlement method, known as when issued, is used for new issues. As the term suggests, settlement is not made until the share scrip is actually issued.

5.4 OPERATIONAL EFFICIENCY AND THE EFFICIENT MARKET HYPOTHESIS

We now turn to the efficiency of the stock market. All major stocks, and many less important ones, are listed on exchanges or on NASDAQ. The reporting systems of these submarkets enable a large number of actual and potential investors to obtain information on prices, volume of trading, and other variables such as the dividends and reported earnings of a company. This fact has important implications for the informational efficiency of the market and, in turn, the potential to profit by trading on various types of information. A market is said to be informationally efficient if at any time (assuming the market is open for trading) all information available at that time is fully reflected in current prices. The concept of informational efficiency must be sharply distinguished from another notion with which it is often confused: A market will be called operationally efficient if trades are executed at the lowest possible cost— that is, if transaction costs are minimal. Before exploring the profound implications of informational efficiency we must say a few words about the more mundane subject of operational efficiency.

OPERATIONAL EFFICIENCY AND THE EFFICIENT MARKET HYPOTHESIS

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Transaction costs can be measured as the difference between the total cost of an item to the buyer and the net proceeds from that same item to the seller. Consider a trade of 100 shares of XYZ at a price of $90 per share. Suppose the buyer and seller are each charged a commission of $75 by their respective brokers; then the buyer pays $9,075 and the seller receives $8,925, so the transaction costs are at least $150. Furthermore, there is normally a bid-ask spread of 1/4 for such a high-priced share on the stock exchange, which means either that the buyer has acquired something whose resale price is only $8,975 or the seller has given up something that it would cost him $9,025 to replace. The bid-ask spread should therefore be added to the commission for a total transaction cost of $175, or almost 2% of the nominal cost of $9,000.32 If there is active competition both in the stock market and among brokers, these transaction costs are presumably minimal and the market is operationally efficient. This assumption is probably satisfied at present, though it would not have been before 1975, when commissions were fixed. Moreover, 2% is not a large fraction of the nominal cost.33 What matters, actually, is not so much how transaction costs in the stock market compare with those in other markets but what effect they have on the frequency of trading. Clearly, a commission of $75 plus a bid-ask spread of $25 is too high to permit frequent sales and purchases of a modest number of shares. It is not surprising, therefore, that individual investors tend to keep their shares for long periods of time. Institutional investors, with their lower transaction costs—typically 3 cents per share or less on large blocks—turn over their portfolios more rapidly, while floor traders and specialists, who have the lowest transaction costs of all, are in and out of the market many times every day. The point of the foregoing discussion is that traders with low transaction costs can respond quickly and easily to any items of information relevant to share prices that reach them. Depending on whether the news is favorable or unfavorable, they will buy or sell immediately without having to worry unduly about transaction costs. Provided there are enough traders with low transaction costs, all information available to these traders will have resulted in virtually instantaneous sales and purchases and will be reflected in current prices. The market will then be informationally efficient. It follows that operational efficiency is a prerequisite for informational efficiency. In a market where transaction costs are relatively large, such as the housing market, we would not expect high informational efficiency. Neither would we expect the stock market to be informationally efficient if all traders had transaction costs as high as those presently affecting small investors using "full-service" brokers. Even though most important news items are widely disseminated, traders with substantial transaction costs may not find it worth their while to act on the news, or even to be "tuned in" to the news.34 Whether the stock market is informationally efficient—that is, whether there is a sufficient number of traders with negligible transaction costs—is essentially an empirical question on which a great deal of research has been done in recent years.

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According to the efficient market hypothesis (EMH), first formulated explicitly in the 1960s but implicit in earlier thinking, the stock market is informationally efficient.35 In fact, it is often tacitly assumed that transaction costs can be ignored altogether. We first discuss the main implications of the EMH and then describe how it has been tested. To begin with, the hypothesis implies that there is no opportunity to earn abnormal returns by investing on the basis of information already available to other market participants; if the market is efficient, this information will already be reflected in the price. In practice, this efficiency means that the market price adjusts so rapidly to new information that almost nobody can profit from it after its release, unless he or she happens to be trading right on the exchange floor. The question to ask is then: For what types of information does this market efficiency hold? Three main variants of the EMH have been distinguished by Fama (1965): 1. The weak form, which considers only past prices 2. The semistrong form, which in addition considers publicly available information 3. The strong form, which looks also at nonpublic ("inside") information 5.4.1 The Weak Form of the EMH, and Technical Analysis

The "weak-form" hypothesis suggests that all relevant information contained in the past history of stock prices will be reflected in the current price. If this variant of the EMH were true, we could rule out so-called technical analysis as an effective method for "beating the market." Technical analysis assumes that stock price movements follow some sort of repetitive (and consequently predictable) pattern. Its devotees plot price movements on elaborate charts to determine where in the pattern the market (or a particular stock) is now; this charting is why technical analysis is also known as "chart trading." The EMH, even in its weak form, considers all this analysis a waste of time; if there were such patterns, they would have been detected long ago, and current prices would reflect this information.36 A great deal of research has been conducted to decide whether or not actual stock prices follow predictable cycles. Time series on stock prices, to be sure, show apparent cycles, but so do randomly generated series; if one tosses a fair coin many times, a run of heads will often be followed by a run of tails. The important distinction is that these cycles occur by chance, and so their occurrence is not predictable.37 One test for the presence of cycles useful in forecasting future price movements is to compute the performance of a "filter rule" of the type that technical analysts might employ. Such a rule might state, for example: "Buy a stock after it has risen 5% from a low (since this signals that an upward cycle has begun). Hold it until the price falls by 5% from its most recent peak (a sign that a


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downswing is under way), then make a short sale. Maintain the short position until the stock again rises by 5% from its most recent bottom, at which point a long position should again be established (to take advantage of the continued upswing)." This is a "5% filter." Following similar work on futures prices by Houthakker (1961), Alexander (1961), and Fama and Blume (1966) tracked the performance of filter rules on data for samples of NYSE-listed equities, using filters between 0.1% and 20%. Trading rules based on filters of greater than 1.5% actually provided lower returns than a simple "buy and hold" strategy for the same stock, even before the rule's higher transaction costs were allowed for. On filters of less than 1.5% it was found that not even a floor trader with the minimum transactions cost of one-tenth of a cent per dollar transacted could net a higher return than the buy and hold strategy. The investigation of filter rules suggests that share prices do not follow consistent cycles over time, so that future prices cannot be predicted from past history. Certain other empirical regularities, however, cannot be so easily dismissed. These center on the phenomena of seasonally.38 The best known of them is the famous "January effect," according to which equity prices tend to rise in that month. Let us look at some data on monthly changes in the Standard & Poor 500 index—more precisely, at changes in the logarithm of the S&P500 from the end of the preceding month to the end of the current month. Over the most recent 25 years (1968 through 1992), the January change in the S&P500 was positive thirteen times and negative twelve times, hardly the stuff from which great fortunes are madel It is true that the mean of the January changes was about 1.3%, well above the mean change of 0.5% in all months over the period of observation, but the difference between these two percentages is not significant by the usual t test. It appears that the January effect is a matter of folklore rather than of fact.39 The data for some other months are actually more interesting. As shown in Figure 5.1, the December changes had a higher mean than the January changes; moreover, in December there were twice as many increases as there were decreases. The largest mean change (in absolute value) occurred in September and was negative; the decreases outnumbered the increases by a wide margin. The monthly mean changes, which in Figure 5.2 were reduced by the overall mean of 0.5% mentioned earlier, are not statistically significantly different from zero by conventional criteria, but a few ratios of increases to decreases may be significant. The existence of monthly seasonality can therefore not be ruled out. Another type of seasonality that has been investigated is weekly, particularly the "weekend effect."40 This effect consists of a tendency for equity prices to fall on Mondays, so it is also known as the "Monday effect." The older evidence supporting the weekend effect was stronger than it was for the January effect, but here practice appears to have caught up with analysis because the weekend effect has not been visible from 1988 on. For this reason, we do not discuss it further (although other days of the week—especially Wednesdays, when prices tend to rise—may be worth another look).

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Figure 5.2 Monthly changes in the S&P500 index (January 1968 through June 1992) While the empirical evidence on filter rules and seasonality does not cast serious doubt on the usefulness of the weak-form EMH as a good first approximation, we cannot be dogmatic as to its validity. A major difficulty in testing all forms of the EMH is that randomness can only be defined negatively as lack of predictability, though the next section presents a way around this difficulty. In a large set of data, such as daily closing prices over many years, there is an enormous number of regularities that could possibly be used in subsequent arbitrage or speculation. Some hidden regularities may yet be brought to light. If so, they are likely to disappear once traders turn them to their advantage, which is apparently what happened to the weekend effect. The reader will have gathered that we do not see much promise in technical analysis. Nevertheless, there are two concepts from this area that are worth knowing, if only because there are many practitioners who pay attention to them. The first of these is known as "support." If a stock in its recent history (say a year) has never fallen below a certain price and has tended to bounce back from that price, technical analysts often assume that the stock will not easily fall below it in the near future. If it does penetrate the "support"—which represents potential buyers waiting in the wings—these analysts expect the stock to fall further. Conversely, "resistance" is the highest price in the recent past, particularly if it was reached more than once. According to many technical analysts, the stock will have difficulty going through the resistance level because of potential selling at that price, but if it does go through, a further rise is expected. In practice, the determination of support and resistance levels often calls for judgment. As a result, econometric evidence on the predictive value (if any) of these concepts is hard to find.


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5.4.2 Do Equity Prices Follow a Random Walk?

If the weak form of the efficient market hypothesis holds, prices will exhibit a "random walk," an important concept of probability theory. A random variable defined at discrete times (for instance, once a day) follows a random walk if its expected value in the next period is the same as its most recent value. Referring to Section 4.2.5, this definition means that x i ,(where i= 1,2, . . . , t,t + l, . . .) follows a random walk41 if for all t

For empirical testing it is convenient form to subtract xt from xt+l and x t _ l from xt. Denoting the resulting differences by A, we then get

Furthermore, it is clear that in Equation (5.1) we may replace the x terms by their logarithms (provided x is positive) so that the 's in Equation (5.2) may be interpreted as logarithmic first differences. Such differences, which are approximately equal to percentage changes divided by 100, have been emphasized throughout this book.42 In the present context, the x's are closing values of a representative price index, specifically the S&P500. In Table 5.3, Equation (5.2) is used to test the random walk hypothesis. Trading days were grouped into three types ("fall," "flat," and "rise") according Table 5.3 Conditional Means of Daily Changes in the S&P500 Stock Index Typea

No. of Observationsb

Mean Changec

Standard Error

t Ratio

Jan '69-'75

Fall Hat Rise All

775 90 768 1633

- .00223 .00009 .00217 -.00004

.00034 .00088 .00031 .00023

-6.6 0.1 7.0 0.2

Jul '75-Jun '82

Fall Flat Rise All

824 100 843 1767

--.00101 .00145 .00100 .00009

.00028 .00065 .00028 .00019

-3.6 2.2

Fall Flat Rise All

1108 145 1272 2525

.00008 -.00045 .00104 .00053

.00036 .00099 .00027 .00022

0.2 0.5 3.8 2.4

Period

Jul '82-Jun '92

"Direction of previous day's price change; "flat" means less than .0005 in either direction. b c

Number of observations of each type.

Mean change in the logarithm of the index.

3.6

0.4

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to the change in the price index.43 Then the mean price change on the next trading day was calculated for each type and divided by its standard error to obtain a t ratio. The reader will recall that a t ratio of about two—the exact value depends on the number of observations—implies that the estimated mean is significantly different from the expected value of zero at the 5% level. The table shows the relevant numbers for each of three periods; the reasons for choosing these periods will become clear in a moment. During the first period, the 775 falls were followed by a mean change of — .00223, with a t ratio of 6.6, so it was highly significant: Falls tended to be followed by further falls. The 768 rises were followed by a mean change of + .00217 (also highly significant), so rises tended to be followed by rises. These figures show that there was considerable persistence in both rises and falls. In the second period, rises and falls also showed significant persistence, but the conditional means and their t ratios were smaller than in the first period. During the third period, by contrast, the mean change following falls was close to zero and not significant, but the mean change following rises was still significant. However, the pattern during the third period was influenced by a marked upward trend (shown in the line labeled "all") that was not present earlier; if this trend is subtracted, the conditional mean following rises is not significant at the 5% level. From this analysis we may conclude that the stock market, as measured by the S&P500, did not follow a random walk during the first two periods but did so in the third period. In other words, the market became more efficient over the years. We must now discuss the rationale for the division into three periods. From 1969 through the first part of 1975, fixed commissions were in effect, causing transaction costs to be relatively high. When fixed commissions were abolished in 1975, the market came closer to a random walk, but some persistence in rises and falls remained. Finally, in 1982 another important change occurred— namely, the introduction of stock index futures (discussed in Chapter 9), which was tantamount to a further reduction in transaction costs.44 The increase in market efficiency shown in Table 5.3 is consistent with these changes in transaction costs, though it does not prove causality. It is somewhat ironic that in the 1970s, when the EMH gained widespread acceptance, there were significant departures from a random walk. Fortunately for financial theory—and for the functioning of our capital markets—the market now conforms closely to a random walk. Reality has caught up with theory. The recent evidence permits us to say that the weak form of the efficient market hypothesis is in general agreement with observed price behavior. This observation does not necessarily mean that prices are constant on average. Instead, equity prices show a long-run upward trend around which they fluctuate randomly. This behavior is sometimes described as a "random walk with (positive) drift."


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5.4.3 The Semistrong Form of the EMH, and Security Analysis

A more stringent hypothesis regarding efficiency is embodied in the "semistrong" form of the EMH. This form postulates that an investor cannot achieve excess returns by trading on any publicly available information (not just price history), because all of this information is rapidly reflected in prices after it has become available. Efficient market theory, in this form, views stock prices as responding rapidly to the receipt by the market of new information bearing on the future returns that the stock is expected to earn. Now new information arrives randomly over time (otherwise it would be predictable and hence not really new). Since stock prices are responding to a random sequence of events, they themselves will again follow a random walk, as under the weak form. Does this random walk imply that Wall Street's security analysts, who study the "fundamentals" of particular firms or industries, do not contribute anything in return for their handsome salaries?45 The answer is "no." Analysts interpret information and sometimes collect new information. Many news items contain only the bare facts; their implications are often unclear, and analysts try to find them. Suppose, for instance, that the XYZ corporation reports earnings of $2.10 per share in the first quarter of 1991 after earning $2.00 in the corresponding quarter of 1990. Is this good or bad news? It depends in part on what the firm had been expected to earn; if earnings of $2.25 had been widely anticipated, the report is disappointing. The meaning of the earnings figure also depends on how it came about. Perhaps the figure was reduced because the firm wrote off its investment in a new product that did not succeed. If so, further analysis is needed to determine its significance for future earnings. The main business of security analysts, therefore, is to add value to raw information. By trading on this enhanced information, their customers cause it to be quickly reflected in the stock price, and they may realize some additional profit during the brief transition from the old price to the new equilibrium. Offset against this, of course, is the cost of enhancing the information. Since it is fairly easy to enter the security analysis industry, which has many participants, we would expect security analysts to earn no more than a competitive rate of return on their total investment. The existence of a security analysis industry, therefore, is not inconsistent with the impossibility of earning abnormal returns by using publicly available data, which the semistrong form hypothesizes. Viewed in this way, fundamental analysis is not a method through which windfall profits are obtained, but a segment of the information-producing industry. Each investor must ask himself or herself whether the additional information produced by security analysts is worth its cost. The answer probably depends mostly on the investor's scale of operations. The institutional investors that now dominate the stock market can hardly afford to do without security analysts and

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often hire their own. For the individual investor, the answer is less clear. By using a full-service broker he or she gets access to a certain amount of "research" (essentially security and technical analysis), but at the cost of paying much higher commissions. As shown earlier in this chapter, the alternative is to rely on discount brokers who provide execution of orders but no analysis. A large number of tests of the semistrong form of the efficient market hypothesis have been conducted by academic researchers. One of the most interesting was reported by Ball and Brown (1968). In this study, an equation was estimated to predict the earnings per share of each of 261 companies over the coming year. The forecast was based on the average trend in earnings in the past plus a deviation from this trend caused by the cycle of average corporate profitability for all other stocks. This forecast was then subtracted from the actual earnings reported at the end of the year. Firms with reported earnings greater than the forecast were placed in one group, while those reporting less than forecast were placed in another group. Now if the stock price responds rationally to publicly reported information, we would expect the stocks in companies reporting unexpectedly high earnings to show above-average returns. Conversely, stocks reporting unexpectedly low earnings would be expected to show below-average price increases and lower returns. This pattern of rational adjustment was exactly what Ball and Brown found, but what is even more interesting is the pattern of the adjustment of share prices. Most of the good or bad information contained in the earnings reports was anticipated by the market, so that the price showed between 85% and 90% of the adjustment before the report was released. The explanation of this pattern implies two conclusions about stock market behavior. First, most of the information contained in the earnings reports had already been quite accurately estimated on the basis of other data, such as macroeconomic conditions and statements by the company and its competitors. Second, the market adjusts very quickly to reflect new information in the price after receiving it. Given the number of well-informed analysts following most major stocks, this occurrence is hardly surprising. The market therefore appears to be informationally efficient in the "semistrong" sense, so that abnormally high profits cannot be made simply by collecting and analyzing publicly available information (after the cost of collection and analysis has been deducted from any gross profits). 5.4.4 How Rapidly Do Prices Adjust to News?

To conclude our discussion of the semistrong EMH, we have to mention a body of evidence that indirectly casts doubt on the assumption of rapid adjustment to publicly available news. This evidence, due mostly to Fama (1965), French (1980), and French and Roll (1986), has to do with the seemingly unrelated question of how time should be measured in the financial markets—in calendar days or in trading days. As discussed in Chapter 8, this question is relevant to the valuation of options, but it has wider implications.


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The main finding of the authors just cited is that prices are much more volatile when the markets are open than when they are closed, particularly during weekends.46 Obviously, some news is generated during weekends, as well as in the early and late hours of weekdays. Indeed, certain types of news (especially about the weather) can emerge at any time, and many government statistics and corporate earnings reports are intentionally released while the market is closed. If prices adjust as quickly to news as the weak-form EMH would have us believe, there would be little advantage in having the stock market open for 61/2 hours, five days a week; it should either be open all the time or rather briefly every day. The greater volatility during trading hours implies that much of the news is not immediately translated into prices. In discussing security analysis we saw that corporate reports often need interpretation by specialized observers. The same is true of many other kinds of news. Suppose, for instance, that a major hurricane is approaching Florida. Apart from the human suffering it will cause, this is obviously bad news for the firms that operate there and for the property insurance industry. It may be good news for home builders and furniture makers who will in due course experience increased demand. But which insurance companies, which home builders, and which furniture makers will be especially affected? This is not a simple question, and it may take many hours—perhaps days or weeks—before the hurricane's effects are fully factored into stock prices. Another example has to do with the release of GDP data by the U.S. Department of Commerce. It might be thought that, since "a rising tide lifts all the boats," publication of a healthy growth rate in real GDP is unambiguously good news for the stock market. In reality, however, traders worry about the effect of GDP on monetary policy. If growth is too rapid, the Federal Reserve may become acutely concerned about future inflation and raise short-term interest rates, which in the past has often affected equity price adversely. As a result, the stock market has in recent years often responded favorably to modestly positive changes in real GDP but unfavorably to any news (not necessarily from the Commerce Department) suggesting that economic activity is picking up. Here again, it will take some time before the implications of new economic data are sorted out. A further reason why the market does not respond instantaneously to news is simply that there is so much of it. The various items that come over the newswires or through the grapevine are often contradictory, leading different traders to arrive at different interpretations. The reconciliation of these conflicting views constitutes the main business of the stock market when it is open. This reconciliation appears to be the reason for the Fama-French-Roll findings that the market is much more volatile when it is open than when it is closed. 5.4.5 The Strong Form of the EMH

The "strong" form of the efficient market hypothesis goes one step further than the semistrong form by postulating that there is no information, publicly avail-

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able or not, that will permit an investor to earn abnormal returns. In other words, it postulates that the current market price reflects all relevant information. Jaffe (1974) tested the strong form by collecting data on periods when there were at least three more corporate insiders selling than buying (intensive selling) and vice versa for intensive buying; such data are available from the Securities and Exchange Commission.47 For a sample of 861 trading observations, he found that the predominant market positions being adopted by insiders outperformed the return on the market (after adjusting for the risks of the individual stocks) by 5% in the 8 months following the intensive trading by insiders. According to this finding, then, the strong form of the EMH does not hold. If it is any consolation, you can still outperform the market for any given level of risk by trading on insider information (although your "return" may well include a prison sentence!). 5.4.6 Conclusions on Informational Efficiency

To conclude, we recapitulate a number of important points developed in the course of our discussion of informational efficiency. There is little or no evidence that stock prices exhibit consistent cycles that could be predicted from past price movements. Prices basically follow a longrun upward trend with random fluctuations around that trend; in other words, a random walk with positive drift. This fact certainly does not imply that stock prices must be fluctuating in an irrational manner. The reason is that prices tend to respond fairly rapidly—but in many cases not instantaneously—and appropriately to new information as it becomes available. Since new information can be either good or bad and is apt to arrive randomly over time, there need not be any serial pattern in the movement of prices from day to day or from month to month. Within this environment it is possible to realize abnormally high profits by obtaining new information and trading on it ahead of the market. To try to do so, however, is to compete in the "information producing industry" against other analysts. This industry is highly competitive, so the excess returns on producing new information are likely to be driven down to the point where they closely approximate the costs. The information generated by the industry is likely to be worth its cost to large investors, but its value to the individual investor is more doubtful. All these arguments imply, in turn, that the informational efficiency of the market is high and that consistently outperforming it is very difficult. Indeed, it may be possible only for those with access to "inside" information. That supposition is not to suggest, of course, that investment in the stock market is not worthwhile; even without "beating the market," the investor's available return may still be quite attractive.48

6

The Determination of Equity Prices

Anyone who can predict security prices with reasonable accuracy and consistency will soon be rich. From the discussion of informational efficiency in Chapter 5, it is clear that persons with this ability are rare indeed. This observation does not mean that financial success in the stock market is impossible, merely that success is less likely to be the result of superior forecasting skill than of the willingness to bear risk, of hard work, of inside knowledge, or of sheer luck. Apart from this rather discouraging insight, does economics have anything helpful to say about the prices of shares and related securities? That is the question addressed in this chapter. We review the most important ideas suggested by economic theory in this area and assess their usefulness in the real world. First we look at two fairly ancient but still popular models of equity prices, one of which views shares as claims to future dividends and the other as claims to the underlying net assets. For the most part, these models look at the shares of individual companies in isolation, not at the market as a whole; that is their weakness, but the asset model in particular provides important insights into aggregate equity values. As an aside to this discussion we also show that aggregate dividends have the intriguing feature of being an approximately constant percentage of National Income, which means that corporate equities offer protection (though not perfect protection) against inflation as well as participation in the real growth of the economy. We then take up the Capital Asset Pricing Model, a discovery of the 1960s that, by considering equities in relation to each other, provided important new insights into the relation between risk and return. A more recent alternative known as Arbitrage Pricing Theory is discussed next. Finally there is a section on stock indexes. 141

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THE DETERMINATION OF EQUITY PRICES

6.1 SHARES AS CLAIMS TO FUTURE DIVIDENDS

A share in a corporation is valuable for three reasons: 1. It entitles the owner to such dividends as the corporation may declare 2. It entitles the owner to a portion of any residual value the corporation may have when it is liquidated or acquired by another corporation 3. Its market price may rise over time The theory of share prices examined in this section focuses on the first of these considerations, while the second is the main topic of the next section. Until further notice, the dividends and liquidation value will both be taken into account. The appreciation mentioned under the third reason may to a large extent be regarded as a secondary effect—a consequence of future dividend actions rather than an independent influence; it is considered only when it is relevant. We start with the simplest case where future dividends are known and paid annually; the time of liquidation and the liquidation value per share at that time are also known.1 The present value of these various payments is then

where Div(t) is the dividend paid at time t, 0 is the present,2 T is the time of liquidation, L is the liquidation value, and rs is the relevant discount rate. Since in this initial example the dividends and the liquidation value are assumed to be known, the discount rate should be a default-free rate. The yield on long-term Treasury bonds is usually appropriate because equities are also long-lived securities. Although the assumption of certainty is obviously unrealistic, it is instructive to pursue this case in more detail. To begin with, we note that if the liquidation time T is at all distant, the final term in the series will normally be small, since it is divided by a high power of the discount factor (1 + rs). Thus if the risk-free rate is 5%, then for T= 100 the liquidation value (plus the final dividend) is divided by (1.05)100= 131.5: Of every $1 of liquidation value, less than 1 cent appears in PVDL. It is only when the liquidation value is large and/or liquidation is expected in the near future that the actual magnitude of L makes a significant difference; in that case, the model explained in the next section is more appropriate. There we use the fact that the liquidation value vanishes when the corporation is assumed to have an infinite life. 6.1.1 Steady Growth in the Dividend

Still retaining the certainty assumption, let us look at an important special cases of the PVDL equation. Instead of assuming each dividend to be known sepa-

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rately, it often makes more sense to postulate growth at a given rate to prevail between now and the liquidation time T, so we have

The growth rate can then be combined with the discount factor to provide an alternative equation for PVDL:

where T is again the distant time at which the company is assumed to be liquidated. It is instructive to look at the case where T approaches infinity. As pointed out earlier, the present value of L then goes to zero and only the dividends matter. The present value of all dividends (including the current one) is denoted by PVD (to indicate the suppression of L); it can be evaluated by the well-known formula for the sum of an infinite geometric series:

However, previous formulas for PVDL did not include the current dividend Div(0), which must therefore be subtracted:

Clearly Equations (6.3) and (6.4) do not make sense if g rs, so we must assume that the growth rate is less than the discount rate. Suppose, for instance, that rs = 0.1 and g = 0.05; then the last expression is equal to 21, so the implied stock price is 21 times the next dividend. In the financial markets it is customary to invert the price-dividend ratio, thus obtaining the "dividend yield," usually expressed as a percentage. In formula:

In this example the dividend yield is 4.76%, a plausible value.3 The reader can also verify that when g = 0 the dividend yield equals the discount rate; this case applies to a preferred share with an infinite life issued by a corporation whose survival is not in doubt. The last proviso, which applies to all the formulas in this section, is not as preposterous as it may seem, since the contribution of very distant dividends to PVD is negligible.

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Figure 6.1 shows that the price-dividend ratio is quite sensitive to variations in g. For a given value of rs, the relation between g and the yield is almost, but not quite, linear. As pointed out by Barsky and DeLong (1993), this sensitivity may explain, incidentally, why share prices fluctuate so much: Expectations of future growth rates of dividends are quite variable. If a firm comes out with disappointing quarterly earnings, for instance, this circumstance will affect the expected growth rate of dividends and will often precipitate a sharp downward correction in the stock price. It is not uncommon for an unpleasant surprise in earnings to slash the price by as much as 50% in one day. The main implication from the steady-growth model is that the dividend yield on one company's shares will be smaller than that on another company's shares if the first company's dividend is believed to grow faster than the other dividend. Most investors, however, will be more interested in the rate of return, which is the sum of the dividend yield and the relative price change. The latter is found by observing that in Equation (6.5) the right-hand side is independent of time and that Div(0) is always the most recent dividend paid, again regardless of time. Thus the equation holds just as well in 1992 as in 1993, but in 1993 the dividend is (1 +g) times larger than in 1992, so the 1993 price must be the same multiple of the 1992 price. The relative price change, therefore, is simply g. It follows that the rate of return equals

Some experimentation with plausible numbers for rs and g will show that Rs is not very sensitive to g, which means that the rate of return (unlike the dividend yield) is approximately independent of the growth rate of dividends.

Figure 6.1

The dividend yield as a function of the growth rate and the discount factor

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Before we leave the steady-growth model a word of caution is in order. In the real world, corporations and their dividends do not grow at constant rates. This fact was shown long ago by Little (1962) from a study of British companies and was confirmed by Brooks and Buckmaster (1976) for U.S. firms; it no doubt remains true today. The dividends paid by a particular corporation, or by all corporations together, may well have a statistically significant trend, but there is bound to be considerable variance around this trend. The steady-growth model does not take this variance into account—which would be mathematically possible but difficult—and is therefore too incomplete to be taken at face value. Yet the sensitivity of stock prices to expected growth (mentioned in connection with Figure 6.1) suggests that the model continues to be influential. 6.1.2 Aggregate Dividends, Earnings, and Inflation

In Chapter 2 we stressed the importance of inflation in determining the performance of the financial markets. We showed that through the "Fisher effect," bonds offer some protection against inflation, but that nevertheless the ex-post real return on government bonds has sometimes been negative. It is interesting to look at corporate equities from this point of view. The lower curve in Figure 6.2 shows that during the period since World War II the ratio of aggregate dividends to National Income has been roughly constant at around 3% despite highly variable inflation. In that sense, corporate

Figure 6.2

The share of dividends and corporate profits in National Income (%). Source: National Income and Product Accounts, from various issues of the Survey of Current Business.

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equities have offered a remarkable degree of protection against inflation—more so than bonds. They have also enabled stockholders to participate more or less proportionately in the real growth of the economy. Closer inspection reveals that the ratio of dividends to National Income declined significantly during the early 1970s but that it returned to the level of the 1950s and 1960s by the end of the period. This finding is all the more remarkable because the ratio of corporate profits after tax to National Income (represented by the top curve) was not only quite variable but also exhibited a distinct downtrend, as shown by the straight lines in the graph. These divergent trends mean that the "payout ratio" (the ratio of dividends to profits after tax) has tended to increase over time. The contrast between the relatively smooth dividend curve and the volatile earnings curve in Figure 6.2 has another important implication. Since the correlation between aggregate profits and aggregate dividends is evidently quite low, profits have not been a good predictor of dividends, yet financial analysts pay great attention to profits. Are these analysts barking up the wrong tree? No, they are not. Given that dividends are to a large extent predetermined—even though we cannot say how—undistributed profits are used to strengthen corporate net worth. This is an argument against the basic assumption underlying this section, which was that shares are valued primarily for the dividends they are expected to pay in the future (possibly with some allowance for the liquidation value). Clearly that is not the whole story.

6.2 SHARES AS CLAIMS TO CORPORATE NET WORTH

The approach of Section 6.1 emphasized the income stream that is usually associated with share ownership; here we consider an alternative that looks at the net worth of the firm. An example introduces the basic idea. Suppose a firm, or a group of individuals, wants to enter the supermarket business. There are two possibilities, not necessarily exclusive. One is to open a brand new supermarket, the other is to buy an existing one. The latter possibility can be realized in two ways: either by buying the store itself from its present owners or by buying the entire firm that owns it. The relative merits of these various procedures need not be analyzed here, except for one major consideration: the relative prices. Clearly, buying the firm rather than building a new one or acquiring an existing one will be the more attractive the cheaper the shares. The same consideration is true in another example exemplified by recent takeover activity. An oil company that plans to increase its oil reserves can do so by conducting its own exploration—at great risk—or by buying an already discovered field from its owners, or by taking over another company with substantial reserves. In the case of small or middle-size oil producers,4 oil in the ground is typically the major corporate asset. After allowing for other assets and

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liabilities, it is possible to calculate the valuation for oil reserves that is implicit in the market price for the shares.5 Unless an oil company has promising exploration prospects of its own, it may well decide that buying another oil company is the cheapest method of expanding its reserves. In an informationally efficient market, the shares of companies with valuable assets but low or negative earnings would be priced according to the former. Such companies are said to be "worth more dead than alive," and they are prime candidates for liquidation through merger or otherwise. Investors who are interested mostly in current income from dividends would not buy such companies. The assets that put a company in this category need not be tangible. Thus some companies have tax credits (usually resulting from past losses) that they cannot use for lack of profits but that may become available to a profitable buyer. Conversely, a firm with unused tax credits may seek to take over a profitable company with a view to realizing these credits. It should be borne in mind, however, that the antitrust laws sometimes make it difficult to merge firms within the same industry, and that the Internal Revenue Service may question transactions undertaken only to make tax losses more valuable. The PVDL formula stated in the beginning of Section 6.1 is sufficiently general to cover valuation of corporate equities on the basis of liquidation value rather than future dividends, though the liquidation value is only known with reasonable certainty if a takeover bid is outstanding. The argument advanced there that liquidation can normally be disregarded applies, strictly speaking, only to very large companies (such as General Motors, IBM, and Exxon), whose size makes them virtually impervious to takeover and whose voluntary liquidation is highly unlikely. In recent years, however, many smaller corporations have changed their bylaws to make themselves less vulnerable to "corporate raiders," to use one of the milder terms by which established managers describe those planning to oust them. According to the PVDL formula these measures tend to lower the value of the shares. The notion that share prices are primarily determined by the net value of the underlying assets can be quantified by a ratio known as Tobin's q.6 In its simplest form, the numerator of this ratio is the market value (MV) of an asset and the denominator is the replacement cost (RC) of that asset: q = MV/RC. If q is low—say, well below 1—those who want to increase their productive capacity will find it advantageous to buy existing assets, thus incidentally driving up the share prices of the companies that own these assets. A high value of q, on the other hand, means that it is cheaper to construct new capacity and to finance this investment by selling securities. The resulting interaction between real investment (that is, construction of additional productive capacity) and the financial markets acts as a self-regulating mechanism for both. A firm's assets will have a low q if the firm does not make effective use of these assets. Thus a company that built an expensive retail facility in a lowtraffic area may find it has created an asset whose market value is below its replacement cost. The same facility, however, may be worth more to another

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retail firm that is less dependent on traffic because its customers will seek it out wherever it is. Conversely, a well-located restaurant may be worth much more to its owners than its replacement cost, so q will exceed 1. Pushing this analysis further we can think of q as an indicator of profitability or rate of return. Let Ra be the return on an asset valued at its replacement cost RC, and let r be the cost of capital. Then, assuming for simplicity that the asset has an infinite life, its market value is MV=(Ra*RC)/r, which implies q = MVI RC=Ra/r. Tobin's q can thus be interpreted as the rate of return on an asset relative to the owner's cost of capital. We can also write Ra = q*r. This rate of return Ra on the replacement cost of an asset (or group of assets) can be used in place of the conventional accounting measures of profitability, which are usually based on book value (historical cost) instead of replacement cost. McFarland (1988) simulated the behavior of a conventional accounting measure in comparison with q under different experimental growth and investment conditions. He found that Ra (as defined in the preceding text) had a much higher correlation with true profitability than the traditional measure. When the concept of q is applied to an entire corporation rather than to specific assets, a complication arises—namely, that corporations usually have liabilities as well as assets. If TA stands for a corporation's total assets valued at replacement cost and TL for its total liabilities (excluding common stock but including preferred stock), then its net worth AW is obviously equal to TA - TL.7 Suppose the market value of the firm (the price per common share multiplied by the number of shares) is MV. A prospective buyer of the entire corporation will normally have to assume the liabilities and will therefore have to pay MV+TL for the assets. It follows that q = (MV + TL)/TA. We may compare this calculation with the ratio of market value to net worth shown for nonfinancial corporations in Table 3.3. This ratio will be called ql to distinguish it from q: q l =MV/NW=MV/(TA--TL). With a little algebra it can be shown that q = q1 +(1 —q 1 )TL/TA. It follows that when ql is less than 1 (as it has been in most years for nonfinancial corporations since World War II), q will exceed ql, but q will also be less than 1 because TL will normally be less than TA (otherwise AW would be negative). On the other hand, if q1 exceeds 1, it will also exceed q, but q will still be greater than 1. The reader is encouraged to verify these inequalities and to investigate the effect of changes in the ratio of total liabilities to total assets. Both q and ql are useful in analyzing shares as claims to net worth. The former originated in Tobin's theory of investment and is therefore of a macroeconomic nature, while the latter is more directly relevant to the financial markets. A chart of ql was given in Figure 3.3. It is complemented by Figure 6.3, which refers to q, and also contains an alternative measure to be discussed in a moment. For convenience, the value 1 is added as a horizontal line. Let us first look at the solid curve in Figure 6.3. We see that, after a strong rise in the 1950s, q fluctuated around 1 during the 1960s. It then fell, first slowly, then sharply in 1973-74 as inflation had an adverse effect on share

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Figure 6.3 Tobin's q for nonfarm nonfinancial corporations, and an alternative measure based on historical cost. Note: Farm corporations, which are included in the top curve, were eliminated by assuming that they have the same ql as other nonfinancial corporations. Since farm corporations account for about 2% of the new worth of all nonfinancial corporations, this assumption is harmless.

prices even though it raised the underlying asset values. During the following 10 years q remained between 0.5 and 0.6, but in the middle 1980s q began to rise at an accelerating rate. At the end of 1993 q reached a record of 1.165, while q1 was then at 1.34, also a record. During 1994 both statistics moved a little closer to 1. What does this this story tell us about q (or q1) as a tool for assessing aggregate share values? Although there appears to be some tendency for 'q to settle around 1, as happened in the 1960s and possibly in the 1990s, it cannot be very strong; otherwise it would not have taken q some 15 years to recover from the precipitous drop in 1973-74. One reason for this slow adjustment may be the inability of historical-cost accounting, as codified in the Generally Accepted Accounting Principles (GAAP), to deal with inflation. Since the data used for the solid curve in Figure 6.3 were derived from current-cost accounting, they immediately reflect the rise in asset values due to inflation. Under GAAP this rise is recognized only when the assets are replaced (see Chapter 1). An alternative to q can be calculated from the historical cost rather than the current cost of tangible assets; it is shown as a dotted curve in Figure 6.3.8 Since inflation was positive throughout the period of observation, the dotted curve is always above the solid curve, but it should be noted that the distance between the two curves was largest during the 1970s and early 1980s when the inflation

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rate was unusually high. In those years, therefore, the alternative measure was much closer to 1 than was q. Since most corporations report only according to GAAP, the historical cost of assets may have unduly influenced investors. The downward bias of reported net worth that is inherent in GAAP was corrected in the fullness of time. The "takeover mania," as it was short-sightedly called, reflected a realization by the acquirers that other corporations were worth more than their balance sheets suggested. The large-scale share repurchases discussed in Chapter 3 reflected a similar belief on the part of managers and directors with respect to their own firms. When q returned to 1, takeovers and repurchases declined. Some comment is needed on the historically high values of q reached in the last few years. The balance sheet data from the Federal Reserve do not take account of intangible assets, and it is conceivable that these have grown in relative importance over the years. As an example, consider the computer software industry, which hardly existed 20 years ago. A successful software firm need not have large tangible assets, while the value of its intangible assets often does not show up fully on its balance sheet. If intangible assets have in fact become more important, this may explain why at present q is well above 1. To sum up, the idea that share prices reflect claims to net worth is to some extent supported by aggregate data. The main reason the correlation is far from perfect appears to be twofold: the undervaluation of nonfinancial assets by conventional accounting, and the slowness of the processes by which this undervaluation is eliminated.

6.3 THE CAPITAL ASSET PRICING MODEL

The most powerful framework within which to understand the pricing of shares has proven to be the Capital Asset Pricing Model (CAPM), developed by Sharpe, Lintner, and Mossin in the 1960s. Essentially it asks the following question: If all investors understand and act on the benefits of portfolio diversification and the distinction between systematic and unsystematic risk (discussed in Chapter 4), what does this imply about the prices of the securities of firms that differ in earning capacity and profit volatility? We begin to answer this question by setting out CAPM in its most basic form. Despite the imposition of some rather restrictive initial assumptions, this approach will provide us with some important and workable results. The next subsection explores the removal of a number of these unwelcome assumptions in order to help us understand the robustness of our earlier conclusions in the more complex world of reality: when the model is applicable and under what circumstances we might need to reassess its findings. This exploration suggests that CAPM has quite wide applicability. Our next concern is its implementation and, in particular, how an estimate of the model's key element, the , (beta, also called systematic risk) of each stock, may be

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obtained from readily available data. With theory and data in hand, we then examine the practical implications of these equity pricing results for portfolio management. In Section 6.3.5 we show, however, that despite its theoretical appeal and its importance in financial economics the empirical validity of CAPM is open to serious doubt; this discussion sets the stage for an alternative model considered in Section 6.4. 6.3.1 The Simplest Form of CAPM

In Chapter 4 we developed the concept of a set of efficient portfolios. Each portfolio belonging to this set represents the mix of individual stocks that minimizes the volatility of the return for any desired level of expected return. These efficient portfolios can be designed by taking account of the degree to which returns on the underlying securities fluctuated together versus the degree to which the fluctuation in one offset the fluctuations in another; in other words, they reflect the full benefits of diversification. One of the central assumptions of CAPM is that the market is dominated by risk-averse investors who practice optimal diversification to stabilize their returns. The basic form of CAPM further postulates that all investors have the same expectations concerning the returns on the various securities, and concerning the variances and covariances of these returns. It is also assumed that the market is an efficient processor of information in the sense described in Chapter 5: News that might influence the earnings of firms, or other relevant variables, is rapidly—indeed, immediately—available to all investors at negligible cost, so that it is immediately reflected in estimates of the future mean and variance of returns. Transactions costs are ignored throughout. In its basic form, the model also abstracts from the complexities of "realtime" income and spending decisions. Its derivation is structured on the basis that all investors have the same "single-period" investment horizon over which the real interest rate is fixed. Individuals are assumed to borrow or lend at that rate at no risk regardless of the amount they need to optimize their portfolio decisions. This assumption implies that the net worth of individual investors is irrelevant; even a pennyless trader can hold a portfolio worth millions of dollars, since he or she can borrow its entire value. The application of this final assumption provides us with an efficient portfolio frontier. By choosing a given portfolio Z, consisting of risky assets, and mixing it with varying proportions of investment in the risk-free investment, which returns the guaranteed real interest rate, an investor can achieve any desired level of portfolio risk.9 If 100% of an investor's wealth were loaned, it would earn precisely the risk-free rate. If, on the other hand, 100% were placed in the portfolio Z, he or she would anticipate receiving the "expected return" on that portfolio as calculated in Chapter 4, but with a risk equal to the variance of the return on that portfolio.

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If A represents the proportion placed in the portfolio of equities, and 1 -A the proportion loaned out at the risk-free rate r, the expected return and risk of the joint portfolio would be:

where Ez and Vz are the expected return and variance of the free-standing portfolio of risky assets, respectively. The risk-return trade-off available by choosing different proportions of risk-free lending and the equities portfolio Z are therefore shown to be the straight line rZ in Figure 6.4. This trade-off line may be improved, however, by choosing a different portfolio (such as Y) with which to mix the risk-free investment. Here the trade-off is steeper: It offers a greater increase in expected return for every unit of additional risk. The steepest trade-off curve possible will be obtained by selecting the portfolio of risky assets that lies exactly where a line from the point r is tangent to the efficient frontier. In Figure 6.4 this portfolio corresponds to the risk-return combination M. Suppose now that an investor wishes to accept greater volatility and higher return than is offered by placing 100% of his or her wealth in the portfolio M. The investor could choose one of the portfolios on the original efficient frontier to the right of M. A better (steeper) risk-return trade-off could be achieved,

Figure 6.4

The efficient frontier with borrowing and lending


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however, by borrowing money at the known interest rate and investing it in the portfolio M. In this case, the expected return and associated variance would be:

where Ar is the interest payment on the borrowing while EM and VM are the expected return and the variance of portfolio M. These opportunities are equivalent to a rightward continuation of the straight line running through M to N. When it is possible to borrow and lend at a known real rate of interest, the efficient portfolio frontier becomes the straight line rMN. The individual's net worth and attitude toward risk will then determine the final point he or she chooses on that line. Notice, however, that it does not influence the optimal composition of the equity portfolio M. An individual's wealth and risk preference alter the total size of his or her investment in equities relative to lending or depositing funds at risk-free interest rate, but they have no effect on the best mix of individual equities to buy. This result is known as the separation theorem because it implies that the decision of how much total risk to accept is separate from the decision what equities to buy. According to this theorem, the best combination of individual stocks follows from objective10 factors, namely, the mean and variance of expected return and the covariances between the returns on individual stocks. The subjective decision of how much total risk to accept is implemented by choosing the amount of funds invested in the fixed portfolio M rather than by varying the composition of the equity portfolio. That unique portfolio of equities M is known as the market portfolio. The new "straight-line" efficient frontier derived from this analysis is known as the capital market line (CML). Its equation may be written as follows: E Ep = r+ (Em — r) ( p/ M), where p and M are the standard deviations of the chosen portfolio and the market portfolio, respectively. The slope of the CML shows the compensation offered by the market (in terms of higher expected return) for bearing greater nondiversifiable risk. For any standard deviation of return ( p) accepted by an investor, the CML shows the highest level of expected return offered by the market, as illustrated in Figure 6.5. The slope coefficient itself is known as the market price of risk, or MPR for short:

In the world of CAPM, where diversification is uninhibited by transactions costs, indivisibilities, restrictions on short selling, or lack of information, any investor who fails to reap the full benefits of diversification is, quite simply, a fool. The portfolio he or she ends up with is more risky than it need be, given its expected return. According to the model, the market will pay no premium for shouldering an unnecessary burden by failing to diversify properly.

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Figure 6.5 The capital market line: An example for an interest rate of 5% per annum Let us return to the slope of the CML. Consider the following chain of logic. The CML indicates the amount of extra return offered by the market for every additional point of systematic risk in our portfolio. If we can then measure exactly how much systematic risk an individual stock adds to our portfolio, we could calculate the extra return that the market would offer us in order to buy that stock and include it in the portfolio. What is our portfolio? If we are optimizers (and, as assumed, share the common expectations as to risk and return), we must choose market portfolio M. How much risk does an individual stock contribute to that portfolio if included in the correct proportion? Clearly the unsystematic component of its volatility will net out when mixed with the large number of other stocks in the portfolio. To the extent that it fluctuates in line with other stocks within the portfolio, however, it will exacerbate the total volatility of the portfolio. The correct measure of how much risk a stock on net brings to the portfolio M will be proportional to the covariance between fluctuations in its return and fluctuations in the returns on all other stocks in the portfolio. Specifically, this will be measured by the covariance between an individual stock i and the portfolio M, expressed per unit of the portfolio standard deviation M: coviM/ M. The return compensation for holding the stock will then be equal to the known interest rate r, plus the market price of risk MPR, multiplied by this index of extra portfolio risk: The final expression in parentheses, a measure of the stock's systematic risk, is known to every analyst on Wall Street—and in many other parts of the world— as the beta of that stock. A beta greater than 1 identifies a stock as "aggressive"


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Figure 6.6 The securities market line

in the sense that it is correlated with the market portfolio in such a way that when the market moves in a particular direction, it is likely to be moving even faster in that same direction. Stocks with betas of less than 1 are "defensive" in that they move proportionately less in any particular direction than the portfolio as a whole. A stock with a negative beta actually moves countercyclically with the market portfolio.11 The market portfolio itself moves exactly in proportion to its own fluctuations and so has a beta of 1. These relationships are commonly expressed graphically as the securities market line (SML) shown in Figure 6.6, which has the following equation: Ei = r + where is the beta coefficient for stock i: = coviM/ The SML therefore gives the expected return "required" by the market for holding a particular security, given the risk-free interest rate, the expected return and variance on the market portfolio, and the beta (or systematic risk) of that stock. By providing a required rate of return for a security, CAPM also tells a good deal about how that security will be priced by the market. Suppose that a stock is expected, but far from certainly, to sell for $50 one year from now, including the value of any dividend declared but not paid. At what price should it trade on the exchange today? The Capital Asset Pricing Model helps answer this question. First, it is necessary to obtain an estimate of the systematic risk (beta) of the stock and the expected return on the market portfolio M. Various means of constructing these estimates are discussed later in this chapter. Second, we need a measure of the relevant risk-free rate. In this case the prevailing rate on one-year Treasury securities would be appropriate. This information can then be plugged into the equation for the securities market line to produce an estimate of the required rate of return Ei. Suppose the T-bill rate is 10%, the expected return on the market portfolio is 15%, and the beta of stock i is estimated at 1.5. In that case:

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Et = 10% + 1.5(15% - 10%) = 17.5%. We can then use the following relation between the expected return and the current stock price: Ei = {E(P l ) —P0}/P0, where E(P 1 ) is the expected price at the end of the year and P0 is the current price. Rewriting this equation we have: P0 = E(Pl)/(l+Ei). In other words, the market price now should be equal to the expected future price discounted by the required rate of return (which allows for the systematic risk of the stock). Substituting the numerical values in our example, CAPM would put the current price of the stock at: P0 = $50/(1+0.175) = $42.55. Note that a similar stock with higher systematic risk would have a lower current price in the market. For example, with a beta of 2.0 the corresponding values would be: Ei= 10%+ 2.0(15%--10%) = 20%; P0= $50/1.20 = $41.67. It is also important to observe that the current stock price produced by this calculation depends only on the systematic risk, not on the unsystematic risk, which can be eliminated by diversification. If the "total volatility" of a security is defined as the sum of the systematic and the unsystematic risk, then it is clear that a low-beta stock may well be a highly volatile stock, and conversely. Volatility matters only to the extent it is correlated with the market portfolio. Before leaving the basic version of CAPM just presented to explore some extensions, a comment on the concept of "market portfolio" is in order. Interestingly, it turns out that if the market prices equities according to CAPM, then the market portfolio is made up of all stocks in the market, each in proportion to the total market value of the stock in the particular company that issued it. Thus, if the total value of IBM stock accounts for 5% of the total value of all corporate stocks in the market, then 5% of the market portfolio will be in IBM. Since the market portfolio represents optimal diversification of nonsystematic risk, it follows that all individuals should allocate 5% of their total investment in equities to IBM stock, and similarly for all other stocks (at least in the strict CAPM world). 6.3.2 Extending the CAPM

As we have already noted, the basic form of CAPM involves a number of rather unwelcome assumptions in the sense that they contradict observed reality. In this section we examine a number of extensions to the basic model that allow us to relax some of those assumptions. Fortunately it can be shown that the major CAPM results remain fairly robust. One assumption used to derive the basic CAPM is that all investors hold the same expectations about the future value of stocks and the corresponding variances of returns. Lintner (1970) has shown, however, that the model can be worked through with heterogeneous expectations among investors by expressing expected values, variances, and covariances as weighted averages of the expecta-


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tions of different individuals, leaving the results essentially intact. The major departure from the basic model is that investors with different expectations will choose different portfolios rather than duplicating the same market portfolio.12 A second unwelcome assumption employed in the basic derivation of CAPM is the existence of a risk-free asset with a certain real interest rate at which investors could borrow or lend. As we have stressed a number of times in this book, when inflation is present there is really no such thing as a "risk-free" asset. Even money or government bonds have a risky real rate of return, given the uncertainty surrounding the future rate of inflation. The only truly risk-free instrument in this context would be an index-linked government-guaranteed bond.13 To overcome this difficulty, Black (1972) has presented a version of CAPM where there is no risk-free asset, yet beta remains the correct risk measure. Briefly, the risk-free asset is replaced by a "zero-beta" portfolio whose return shows no systematic correlation with the market. In reality, most stocks are positively correlated with general movements in the market to some degree. We can still construct a zero-beta portfolio, however, by selling some stocks short, so that we lose money when these stocks rise in price and gain money when their price falls. In this way, it is possible to create return streams that are negatively correlated with the market even when the stock price itself is positively correlated. Yet another assumption that needs to be reconsidered is the requirement that investors base their decisions on a single period horizon over which the rate of interest on the risk-free asset (or the return on the zero-beta portfolio) does not vary. In reality, investors tend to have multiperiod horizons over which interest rates and expected returns may fluctuate significantly. In an important 1973 paper, Merton tackled this problem by deriving a version of CAPM that assumed investment and trading occur continuously over time and that interest rates fluctuate. This formulation results in an equation for the required rate of return on a stock very similar to the SML, but with the addition of a second term involving another beta ( ). A stock now has systematic risk not only to the extent that its return fluctuates in sympathy with the market portfolio (as measured by what is now called ), but also to the extent that it is correlated with movements in the risk-free rate. It is this second source of systematic risk that the term involving allows for. Finally, we should mention a recent extension of CAPM that ties in with the discussion of time preference discussed in Chapter 4. The original CAPM looks at individuals only as investors who seek to maximize the return on their assets, which are assumed to be determined by factors outside the model. In reality, individuals are not merely investors; their portfolio decisions are incidental to more important decisions, such as how much to save for their old age and how to be prepared for economic uncertainties prior to retirement. What individuals and their families maximize is not primarily the return on their assets, but consumption during their lifetime (possibly augmented by intended bequests).

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The consumption CAPM (CCAPM), developed by Breeden (1979), views investment in these broader terms. It considers not just the covariance between particular securities and the market portfolio but the covariance between securities and earnings from work. An automobile worker, for instance, would be illadvised to invest in automotive shares—especially in his or her own firm—since they are likely to be depressed precisely when he or she needs cash because of layoffs or part-time work schedules. From this point of view, bonds are a better investment because interest rates are likely to fall (and hence bond prices likely to rise) during a recession.14 Similarly, a firm that has a pension fund for its employees may not serve them well if it invested the fund in its own shares. Although it may also be viewed as an extension of CAPM, Ross' Arbitrage Pricing Theory is sufficiently different to warrant a separate section (6.4). 6.3.3 Estimating Betas

The lynchpin of the basic CAPM and its extended versions is clearly the measure of systematic risk, beta. To make the model operational as a pricing tool, our next task must therefore be to devise a means of obtaining workable estimates of beta for individual stocks. One widely adopted method is to estimate beta from past data on actual returns provided by a stock and the market as a whole. Returns on the stock may be calculated directly from past dividends and price movements. The return on the market is usually approximated by computing the return on some market index such as the S&P500 or Value-Line. Given these data and a measure of the risk-free rate derived from yields on government bonds, multiple regression analysis can be applied to the following form of the SML: Rit -rt= ai + bi{Rmt - rt) + uit, where Rit is the actual return on stock i in each past period t, Rmt is the actual return on a market index rt is the yield on bonds, and uit is a random error term assumed to satisfy the usual assumptions for unbiased and efficient regression estimates of ai and bi. Recall that the theoretical derivation of the SML implies that ai = 0 and that bi will be a measure of systematic risk of the stock i. In fact, most empirical work finds that a i >0—that is, low beta stocks are systematically underpriced compared with what CAPM would suggest. Overall, however, this method appears to have provided useful estimates of beta and is currently employed on a regular basis by a number of major U.S. brokerage houses. The major limitations are twofold. First, past systematic risk behavior is not necessarily a good measure of future behavior. The second, and related, problem is that actual measures of beta derived from this methodology tend to be relatively unstable from one sample period to the next. The main alternative approach is to use a number of fundamental indicators of the underlying firm's operations and financial structure in order to predict the beta of a


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stock. Rosenberg and McKibben (1973) provided some of the main results in this area. In respect of one important parameter of financial structure, CAPM itself implies that the beta of a levered firm will increase linearly with the ratio of debt to equity in its balance sheet. Specifically, it can be shown that = + (1 -TC)(D/E), where / L is the beta of a levered firm, u is the beta of an otherwise identical unlevered firm, TC is the corporate tax rate, and D/E is the ratio of debt to equity in the levered firm's balance sheet. In addition to leverage, Rosenberg and McKibben identify a number of other financial and operating measures that prove useful in predicting beta for individual firms, including their level of liquidity (liquid assets over current liabilities), the importance of fixed plant in the total assets (inability to reduce capacity and fixed overhead during downswings increased the volatility of earnings), growth in total assets and sales, and so on. Once these factors are taken into account, they find that the historical beta has little additional predictive power. Despite this work, however, the accuracy of beta forecasts remains relatively low, rendering the prediction of beta an important hurdle to implementation of the CAPM approach to equity pricing. We return to this subject in Section 6.3.5, where the validity of CAPM is considered in light of recent evidence. For the time being, however, we maintain CAPM as our working hypothesis. 6.3.4 Implications for Portfolio Management

Under the strict assumptions of CAPM, the resulting separation theorem suggests a very straightforward approach to portfolio management: Simply divide the total investment in equities according to the proportions implied in the market portfolio so as to reap maximum benefit from diversification, then mix this portfolio with an investment in the risk-free asset so as to reach the desired combination of risk and expected return. In fact, the advent of "index funds" in recent years (a way of roughly emulating the market portfolio) has come close to putting this approach into practice. Many investors and portfolio managers, however, partly justified on the information generated by their own research operations, believe they are able to identify stocks that will outperform the market. Of course, if they could be certain of abnormally high returns from these investments, it would clearly make sense to invest their entire portfolio in such stocks. Except for insider trading, however, the most that research is likely to identify is an expectation of abnormal return (i.e., above the "required return" estimated by the SML given its beta), an expectation that itself has some degree of uncertainty. In this case, we can think in terms of an "expected abnormal return," which is the investor's best guess, and some "variance of abnormal return" around this expected value. Placing a higher proportion of our portfolio in these "active" stocks will move us away from the optimal diversification associated with the "passive" market portfolio and thus increase the total variance of return our equity invest-

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ment. In other words, it leads us to accept some unnecessary systematic risk. At the same time, because we expect some abnormal return by investing in the active stocks, the overall expected return on the unbalanced portfolio will be higher. The question then becomes, How much should we unbalance our portfolio, if we believe we can identify some stocks on which we expect abnormal returns? To answer this question, the investor or portfolio manager must estimate the mean abnormal return he or she expects (EAi) for each active stock i and the variance associated with this estimate (VAi); essentially the degree of confidence about whether or not an abnormal return will eventuate. It has been shown (Harvard Business School, 1971) that the proportion of each stock in the active portfolio (ai) should be such that: ai = (EA i /VA i ), where A is a constant that will be discussed in a moment. The interpretation of this result is quite straightforward. The higher the proportion of the active portfolio placed in the ith stock is, the larger its expected abnormal return (EAi) and the smaller the variance of this expected abnormal return (VAi) will be; that is, the more certain the abnormal return is. The optimal split between the passive market portfolio and the active portfolio is then given by the equation

where F is the fraction of the total amount to be invested, which should be placed in the market portfolio. It will be noted that the beta of each active stock appears in this second formula, because the market portfolio is effectively acting as a hedge against the volatility of the active stocks. If these active stocks have high betas (i.e., move closely in sympathy with the market portfolio), then the market portfolio is a less attractive hedge, hence less of it will be held. Conversely, low betas indicate that the market portfolio is a good hedge against the volatility of the active stocks and so it will make sense to buy more of the market portfolio. What these two equations actually define is a new CML, taking into account our expectations about abnormal returns. The only unknown that remains to be determined is A, which indicates where we end up on the CML: how much we place in equities and how much in the risk-free asset. As before, this figure is determined by the individual's subjective risk-return preferences. Once the desired overall risk and expected value mix is chosen, we can solve for A, which in turn may be substituted to compute the proportions F (investment in the market portfolio) and ai (the fraction invested in each individual active stock). An example serves to elucidate the preceding approach. Suppose you have identified three stocks, ABC, MNO, and XYZ, that you believe will outperform the market over the coming year. The unsophisticated investor may simply conclude that the entire portfolio should be placed in these stocks. As we have seen, however, this decision would involve accepting a high level of unsystematic risk


Table 6.1

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Sample Assessments of Abnormal Return Estimated Excess Return

Stock

Mean

Variance

Beta

ABC MNO XYZ

5% 2% 4%

200 80 20

2.0 1.0 0.5

Notes: Risk-free rate =10%; expected return on market portfolio = 15%; variance of return on market portfolio =25.

that could otherwise be diversified away. Not surprisingly, in a highly efficient and generally sophisticated market such as that for stocks, your belief must be given more precise empirical form before it can be successfully put into practice. You might produce the subjective estimates of mean abnormal return and the variance of that return shown in Table 6.1. The next step is then to estimate or collect from published sources values for the beta or overall systematic risk of each of your chosen stocks, shown in the final column of the table. By direct substitution into the equations for the ai already shown, we are able to produce the expressions, still containing one unknown A, given in the first column of Table 6.2. We can then substitute into the equation for the optimal proportion in the market portfolio:

Suppose, then, that you wish to keep a core 10% of your portfolio invested in a "risk-free" asset such as T-bills. With this information we can use the fact that the portfolio proportions must sum to 100% (i.e., 1.0), hence:

where RF is the proportion in the risk-free investment. Substituting the values in Table 6.2 we have 0.275A + 0.175A + 0.1 = 1.0, which implies A = 2.0. Using Table 6.2 Optimal Portfolio Composition Asset

Intermediate Calculation

Optimal Proportion

ABC MNO XYZ

0.05A 0.025A 0.2A 0.175A Chosen on basis of risk preference

10% 5% 40% 35% 10%

Market portfolio T-bills

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this value for A, we can then compute the optimal proportions, completing the final column of Table 6.2. Note the high proportion placed in XYZ, reflecting the fact that a substantial abnormal return (4%) is expected with considerable certainty (a relatively low variance of 20).15 6.3.5 The Validity of CAPM

So far we have assumed that CAPM holds at least approximately, and we have explored its implications and ramifications. This means that we have tentatively accepted its assumptions—for the sake of argument, as it were. Any model simplifies reality in order to arrive at conclusions. If a model is to be useful, these simplifications should be relatively harmless, in the sense that minor departures from the assumptions do not seriously affect the conclusions. How do we know if CAPM is valid in the real world? The essence of CAPM is expressed by the SML, which says that the return on any security is a linear function of its beta. In a recent paper, Fama and French (1992) looked closely at this functional relation in a large cross section of equities. Their findings can only be described as devastating: There appears to be no connection between beta and return at all. They explain the return on the securities in their sample by two other factors, namely, the size of the corporation and the ratio between market value and book value.16 When these two factors are taken into account, beta adds nothing to the explanation. Since they deal carefully with the problems in estimating beta discussed in Section 6.3.3, their surprising results cannot be attributed to errors of measurement. Where does this finding leave CAPM? The work of Fama and French is so recent that detailed reaction from other experts is not yet available. It is too early to assign CAPM to the scrap heap, but obviously its status as the "ruling paradigm" in financial economics has been undermined. Fortunately there is an alternative model, to which we now turn.

6.4 ARBITRAGE PRICING THEORY: AN ALTERNATIVE APPROACH

The CAPM has many attractive features and, as we have already shown, must be credited with a number of potentially useful applications in the area of securities pricing and portfolio management. At the same time it is also clear that, even in its extended form, CAPM requires some unwelcome assumptions and that the central concept of beta has not stood up in recent tests. There is also the problem, mentioned in Section 6.3.2, that when an inflationary environment renders all real returns uncertain, the model in its simplest form cannot be subjected to a decisive test of validity. In 1976, Ross presented an alternative, more general model with a number of similarities to CAPM, which he called the "Arbitrage Pricing Theory." The

ARBITRAGE PRICING THEORY: AN ALTERNATIVE APPROACH

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name reflects the simple, yet powerful, principle on which the model is based: that a portfolio with no risk, which mixes long and short positions in such a way that it requires no net investment of wealth, must earn zero return in a market with no transactions costs. In other words, the prices of stocks in a market should be such that it is not possible to make a profit by simply arbitraging between different stocks without making any net investment or accepting any risk. If this were not the position, investors would quickly identify the opportunities to make "pure profit" and the resulting trading would cause prices to adjust until these opportunities were eliminated. The model begins with the assumption that the actual return realized on any security is equal to its expected return plus a series of unexpected impacts on return, each of which is caused by some uncertain "risk factor" (such as inflation), each multiplied by a coefficient that reflects the systematic degree of sensitivity of the stock to that risk factor. Mathematically, this may be written as:

where Ri is the realized return on security i, Ei is its expected return, represents the sensitivity of the actual return on i to the jth risk factor (Fj), and ui is a random "white noise" term that averages to zero. This evidently has a family resemblance to the beta of CAPM but should not be confused with it. By combining the equation just given with the condition that there should be no opportunities for pure arbitrage profits, Ross was able to derive the following expression for the expected return on a stock:

Intuitively, this implies that the expected return on the ith security is equal to a constant return (the return on a risk-free investment), plus the sensitivity of the return on the stock to each risk factor (the ), times the "market price" or compensation offered by the market for accepting more exposure to that type of risk (the ). Provided we have data on more stocks than there are relevant risk factors, it is possible to estimate the betas or "loadings" (from which the underlying movements in the risk factors can then be reconstructed) by a multivariate statistical technique appropriately known as "factor analysis." Tests using this methodology by Roll and Ross (1980) and Chen (1983) have found that the differences in estimated betas (sensitivities to different sources of risk) perform well in explaining variations in returns across securities and improve on those derived from CAPM. This finding leads us to the conclusion that there are other types of systematic risk that are relevant to the determination of stock prices in addition the nondiversifiable risk associated with movements in the return on the market (which is the source of risk measured by the traditional CAPM beta). Little headway has been made in applying the APT approach, however.

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The basic stumbling block is that the model does not identify the risk factors in terms of measurable variables such as inflation or GNP growth.17 Moreover, even the actual factors estimated in empirical models do not appear to be readily recognizable in terms of such familiar variables. We are therefore unable to forecast the movements in the risk factors in a way that could make the model useful for predictive purposes. Despite its faults, CAPM thus remains the basic workhorse for computing the "required" rate of return on a stock in any period, given an estimate of its systematic risk.

6.5 APPENDIX: STOCK INDEXES

When we overhear someone in the subway saying "the market was down 10 points," most of us know which market he or she meant, and many of us also know what the "points" refer to—namely, the change in the Dow Jones Industrial index (DJI). This index is the oldest and most popular indicator of equity prices but it is not the only one and certainly not the best. Like all price indexes, the Dow is intended to summarize the diverse movements of a number of prices—in this case, the prices of the thirty stocks that are included. Since at present more than 6,000 stocks are regularly traded on exchanges or in the overthe-counter market, one may wonder how the price changes in so many equities can be adequately summarized by an index based on so few. 6.5.1 The Three Main Indexes

First look at Figure 6.7, where annual averages of three commonly used stock price indexes are plotted from 1949 to 1990. In addition to the DJI, these are the New York Stock Exchange Composite Index, covering all equities listed on that exchange, and Standard & Poor's index of 500 stocks (S&P500). The vertical scale is logarithmic; the difference between the high and low values is so large that the ordinary linear scale would not be suitable. The use of logarithms also makes it possible to show the percentage growth rates over the period, which correspond to the slopes of the three straight lines. It is clear that the annual percentage changes in the three indexes are highly correlated and that their growth rates are very similar.18 Actually the growth rates of the S&P500 and the NYSE Composite are virtually the same, but the growth rate of the DJI is significantly smaller: In the 1950s, the DJI was typically about eleven times the S&P500, but in the 1980s it was only about eight times the S&P500. This difference in performance is due to two factors that cannot easily be distinguished. The first factor is the nature of the stocks covered by the two indexes: The DJI includes thirty large corporations, many of which are of the "smokestack" variety—these are in capital-intensive industries that have generally not done as well as the "high-tech" companies, of which there are relatively

APPENDIX: STOCK INDEXES

Figure 6.7

165

Three major stock indexes. Source: Data from Economic Report of the President, February 1995, table B-96.

more in the S&P500 (and also in the NYSE). The second factor has to do with the way the indexes are calculated and requires more detailed explanation. Most price index numbers, including the three mentioned at this point, may be represented by the formula

where t is the current time period, 0 is the "base period," I0 is the value of the index in the base period, n is the number of components (P), and wi (i= 1 to n) is the relative importance or "weight" of the ith component.19 The DJI is an "unweighted" index, which means that all of the wi are equal to 1. In the S&P500 and the NYSE Composite, by contrast, the weight of each stock reflects the number of shares outstanding; thus large companies with many shares, such as IBM or AT&T, have a much heavier weight than other stocks. Now we examine the effect of a stock split. Suppose Texaco, a component of all three indexes, splits 2 for 1 (as explained in Chapter 3), and suppose, furthermore, that before the split there were 10 million shares outstanding and that the price was $50 per share. After the split, there are 20 million shares outstanding and the price is $25 per share; the market value remains at $500 million.20 In the S&P500 and the NYSE Composite, the weight of Texaco, reflecting the number of shares, will simply be doubled, thus leaving the overall value of the index unchanged, since the price of Texaco shares (both in the current and in the base period) is simultaneously reduced by one-half.

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In the Dow Jones, however, the weight is always unity so it cannot be doubled. Instead, the value of I0 in the above equation is adjusted so as to leave the value of the index unchanged. Suppose the prices of the twenty-nine other stocks in the DJI added up to 600; then the DJI was at 650 before the Texaco split. After the split, the Dow would be 625 if no adjustment were made. Consequently, Dow Jones multiplies I0 by 650/625 = 1.04. Somewhat confusingly, the current value of I0 is known as the "multiplier," and we see that it changes every time a component of the DJI varies the number of outstanding shares by a stock split, stock dividend, or otherwise.21 The compilers of the S&P500 and the NYSE Composite also have to deal with another problem—namely, sales and purchase by a corporation of its own shares. From Chapter 3 we know that significant sales of shares are mostly associated with new issues. A stock dividend also increases the number of shares outstanding, and so does a Dividend Reinvestment Plan under which stockholders may choose to receive their dividends in the form of additional shares. Yet another possibility is that the company's convertible securities (bonds or preferred stock) or its warrants are converted into common stock. The treatment of net issues, whether positive or negative, in the weighted stock indexes (particularly the S&P500 and the NYSE Composite) is basically simple and the same for the various possibilities discussed in the preceding paragraph. Suppose a corporation has 100 million shares outstanding and issues 10 million new shares. Its weight in the index is then increased by 10%. If instead the same corporation were to buy back 10 million shares, its weight would be reduced by 10%. Could this straightforward procedure be a source of bias? It could be if the decision by a corporation to issue new shares, or to repurchase some of its outstanding shares, affects the market price of the stock. This effect will occur if the demand curve for the shares involved is downward sloping; in other words, if there is price elasticity.22 A new issue will then tend to depress the market price and a repurchase will tend to enhance the market price. The magnitude of this effect will vary inversely with the price elasticity of demand for the stock; thus if a new issue raises the number of outstanding shares by 10%, then the price, everything else remaining the same, will fall by 10% divided by the price elasticity. If the price elasticity is very high (that is, if the demand curve is nearly flat), the price effect would be negligible, but if the elasticity is two, the stock price would fall by 5%. In the latter case this would be approximately equivalent to a 1.05 for one stock split, but the corresponding adjustment in the weight is not made. Under the same elasticity assumption, a repurchase of 10% would be approximately equivalent to an 0.95 for one reverse split. Since these adjustments for implied splits are not made, it follows that corporations issuing new shares get too large a weight in the index, whereas repurchasing corporations get too small a weight. We are not proposing that such adjustments be made; that would be difficult since the relevant price elasticities are not known. It is also clear that any bias is small in the short run. It may be

APPENDIX: STOCK INDEXES

167

significant if net issues are either positive or negative over a long stretch of years, as they were in the 1980s. In any case, it should be realized that stock indexes such as the S&P500 or the NYSE Composite do not necessarily give an accurate picture of average share values in the long run. 6.5.2 Some Other Stock Indexes

None of the three indexes discussed so far covers more than a fraction of the more than 6,000 equities that are currently traded on the exchanges or over the counter. Because the prices of most equities are positively correlated, this limitation is not as serious as it may seem. Nevertheless, there is a need for more comprehensive indicators. The most comprehensive of these is called the Wilshire Associates Equity Index, though strictly speaking it is not an index number at all. It is an estimate of the total value of all stocks traded in the United States and therefore corresponds to the numerator in the preceding equation.23 On April 12, 1991, for instance, the Wilshire "index" had a value of $3,647 billion. This value was 10% higher than a year earlier, but it is not clear that comparisons over time are meaningful. Other fairly comprehensive measures are the Value Line Index and the Russell 3,000 index. There are also many stock indexes that cover particular classes of stocks. Thus, the NYSE Composite index has counterparts on the American Stock Exchange and on NASDAQ (the automated quotation system covering the OTC markets). Supplementing the DJI, which refers to "industrials" (rather broadly defined), Dow Jones also has indexes for transportation and for utilities. The Wall Street Journal (owned by Dow Jones) publishes daily indexes for a great many industries. In addition to the Russell 3,000 index just mentioned, there is a Russell 2,000 index that covers smaller companies. Recently, Standard & Poor has started publishing an index of 400 smaller stocks not included in the S&P500; it is often referred to as the "Mid-Cap" index, where "cap" is short for "capitalization." Among foreign stock indexes, the most important ones are the Financial Times FT-SE100 index of 100 large shares quoted in London and the Nikkei index of Japanese shares. Since price movements on the world's stock markets are correlated, these indexes are closely watched by professional traders in the United States. Various attempts have been made to develop worldwide stock indexes, but so far none has gained general acceptance. Such indexes are of interest to investment managers because the principle of diversification (emphasized in Chapter 4) suggests that foreign equities should be included in optimal portfolios, particularly because some of them may have low correlations with domestic equities—and sometimes higher returns as well. A widely accepted international stock index would be a more meaningful indicator of investment performance than the purely domestic S&P500.

_7 Security Analysis

In Chapter 5 (Section 5.3.2), we stated that security analysis is consistent with market efficiency because it interprets the news that reaches the market from firms and other sources. In this chapter we discuss in more detail how this interpretation is accomplished, drawing mostly on three sources: the economics of industrial organization, data on industry growth, and accounting.

7.1 SECURITY ANALYSIS AND MARKET EFFICIENCY

In an informationally efficient market, all publicly available information will be rapidly reflected in the market price of a security. As noted in Chapter 5, there is considerable evidence indicating that major securities markets exhibit a high degree of informational efficiency. Does this evidence imply that security analysis is a waste of time? The answer is an emphatic "no." It is precisely because there are a large number of qualified people generating relevant information by analyzing securities and trading on the basis of this new information that the market is so efficient. As new information becomes generally known in the market, the price will adjust to reflect it, and in the process of this adjustment those with the new information early (notably those who generated it) will make money. If the new information is favorable to the stock, for example, the new market price will be higher. Those who were first to have the information will have bought early (before the rise) and thus profit as others in the market become aware and traders adjust their prices upward. If the market is efficient and adjusts quickly, all the better, since profit will come sooner. 168

A MODERN VIEW OF SECURITY ANALYSIS

169

What market efficiency does imply, however, is that if the investor is to be rewarded for time and money spent on security analysis, he or she must obtain information that is both relevant and new (i.e., not already known to the majority of active traders in the market). Clearly, security analysis is also profitable only if the value you realize from the new information exceeds what it costs you to produce it. All of the above is just common sense, but it has important implications that are not always recognized by actual and prospective investors. These implications are best understood by likening involvement in security analysis to a firm competing in an industry, in this case an industry that produces information. As in any industry, good profits are based on having some source of advantage over competitors. Some competitors have the advantage of rapid access to new information as it becomes available: Floor traders, for example, know almost immediately the short-term movements in the prices of the securities they follow. They can also act on this information "on the spot," causing the relevant information to be immediately incorporated into the price. It is not surprising, therefore, that so many studies have concluded that off-floor analysts gain little new information by looking at reported daily, weekly, and monthly price changes, and that technical trading rules fail to produce a net profit after transactions costs. Other competitors, such as the large brokerage houses and mutual funds, have economies of scale in systems for rapidly collecting, processing, and distributing information on their side. The fixed costs of computerized databases, for example, can be spread by selling the information directly or indirectly (through a package of brokerage or funds management services) to a large number of customers. Yet other individuals and firms compete on the basis of superior techniques for security analysis or specialized knowledge of a particular industry. Outstanding analysts can command annual salaries in the milliondollar range. In summary, security analysis is still useful in an efficient market and it can be the source of significant profits for the analyst (or the analyst's employer), provided she or he has some advantage that enables her or him to compete against others in what is, in fact, an information-providing industry.

7.2 A MODERN VIEW OF SECURITY ANALYSIS

The price of a security in an efficient market will be the present value of the future cash flow that it is expected to generate, discounted at a rate that corresponds to the security's beta. The objective of security analysis is basically to identify current profit and cash flow, to forecast how profit and cash flow will grow or decline in the future, and to assess the risk of fluctuations around this forecast, including the risk that the cash flow will be interrupted due to liquidation, bankruptcy, legal injunction, and the like.

170

SECURITY ANALYSIS

During the period of relatively stable growth for most corporations in the 1960s, the emphasis was placed on projecting a firm's income statement for the current period in a roughly linear fashion, at a growth rate determined by projected growth in the economy as a whole, plus some adjustment for the particular industry in terms of demand for its class of products and sensitivity to the business cycle. At the individual firm level, attention was heavily directed toward the firm's ability to expand its physical, human, and financial resources to meet new demand, because this ability represented the most important constraints to increased value. Much of the relevant information could therefore be gleaned from the firm's existing capacity utilization, its plans for expansion, and its record of managing growth in the past. Potential growth is still important, and it is discussed (on the industry level) in Section 7.2.2. In the more volatile economic climate of recent years, however, there have arguably been greater divergences between the performance of individual firms than can be attributed to industry growth alone. In other words, differences between the individual firms within any one industry appear to have become more significant. In response, modern security analysis has focused increased attention on the sources of competitive advantage enjoyed by the individual firm and the longer-run defensibility of those advantages, not only against established competitors but also against foreign competition and entry by firms innovating or diversifying from other industries. Analysts have increasingly looked toward theories of industrial organization and corporate strategy, combined with a detailed knowledge of recent trends in an industry to aid them in estimating companies' earnings prospects and their prospects of being taken over by other firms. Modern security analysis is thus as much a strategic assessment as it is a more traditional accounting analysis of the firm. 7.2.1 Macroeconomic Developments and Changes in Regime

Although this chapter is mainly concerned with analysis on the firm and industry level, it must be recognized that virtually all firms are affected by macroeconomic developments, particularly the real growth of the economy, the inflation rate, and the various interest rates. Some of these factors have already been discussed in Chapter 2 and elsewhere. Their impact will often differ according to the industry or industries in which the firm specializes, so we come back to this in the next section. Furthermore, most American firms of significant size are affected by developments abroad, whether through exports or imports or because they have foreign operations. If so, their performance depends not only on economic conditions abroad but also on another set of macroeconomic factors discussed in Chapter 2, namely exchange rates. In the case of imports and exports, changes in exchange rates will alter the firm's ability to compete; an importer of Japanese cars, for instance, will be adversely affected by a rise in the yen while the same


171

rise will help an exporter of American soybeans to Japan. Foreign operations are affected in a different way: The dollar value of earnings from abroad is converted at different rates. Thus if an American company operates in Britain, its earnings from there (or the dividends it receives from its British subsidiary, if the latter is organized as a separate corporation) will be worth more the higher the value of the British pound in terms of dollars. Individual firms will also be influenced by what are sometimes called "changes in regime," where "regime" stands for the general rules under which all firms operate. The most important examples are the tax code and restrictions on international trade. As regards the tax code, it is clear that a change in the rate of corporate income tax will affect all corporations.1 Other changes in taxation may have a more selective impact, which the security analyst will have to determine. Thus an investment tax credit, permitting firms to deduct a fraction of their expenditures on capital formation from their tax bill, was in force from the 1960s to the 1980s and its reintroduction was considered by the Clinton administration. Such a credit is of special importance to capital-extensive or rapidly growing firms. Another tax change that has often been talked about is elimination of the double taxation of dividends—once under the corporate income tax and once under the individual income tax. In some countries, but not in the United States, shareholders receive an income tax credit for the corporate tax already paid on their dividends. If such an arrangement were introduced here, corporate equities would become a more attractive investment. On the international side, the trend toward liberalization of trade and capital movements since World War II has been favorable for many American firms, the exception being those firms that saw their previous protection (in the form of tariffs or quotas) being eroded. Further progress toward free trade remains to be made, and its effect on individual companies needs to be carefully analyzed. 7.2.2 Industry Growth

As shown in Table 7.1, the major sectors of the U.S. economy have grown at quite different rates since World War II.2 The agricultural sector stands out with the slowest growth rate. The service sector grew the fastest; other rapidly growing sectors were communications and finance (including insurance and real estate). The last column sheds light on the variability of growth in each sector. We see that growth in the agricultural and mining sectors was highly variable, while services and retail trade had much steadier growth. As one would expect, durable manufacturing, which supplies mostly investment goods and durable consumer goods, is more volatile than nondurable manufacturing. Although a full explanation of these differences is beyond our scope, it is important to understand the main factors determining the growth rate of a sector: 1. The income elasticity of demand may be defined as the percentage change

172

SECURITY ANALYSIS

Table 7.1 Growth Rates of National Income in Major Sectors of the U.S. Economy, 1946-1989 Sector National Incomec Domestic sectors Private sectors agriculture, forestry, and fisheries mining construction manufacturing durable goods nondurable goods transportation and public utilities

transportation

communications electric, gas, and sanitary wholesale trade retail trade finance, insurance, and real estate services Government and government enterprises

Logarithmic Growth Ratea

Standard Deviationb

0.073 0.073 0.072 0.039 0.058 0.082 0.065 0.068 0.060 0.070 0.060 0.086 0.082 0.072 0.064 0.084 0.092 0.075

0.035 0.035 0.039 0.118 0.129 0.059 0.063 0.081 0.050 0.035 0.050 0.034 0.055 0.044 0.030 0.029 0.024 0.057

a

Mean annual change in the logarithm of each sector's contribution to National Income.

* Standard deviation of the logarithmic changes. c

Without capital consumption adjustment (see Chapter 2); includes factor payments to and from the Rest of the World, which are excluded from the other items. Source: Calculated from NIPA table 6.03B using diskettes from Bureau of Economic Analysis.

in the consumption of a product (or group of products) associated with a 1% change in income. It is easy to show that this elasticity also equals the ratio of the growth rate of consumption of that product (or group) to the growth rate of income. Thus if the income elasticity of food demand is 0.5, then the growth rate of food consumption—everything else remaining the same—is one-half the growth rate of income. In fact, it was discovered long ago that the income elasticity of food demand is less than 1, an empirical regularity known as Engel's Law. This fact explains, at least in part, why the agricultural sector, whose main product is food, grows so slowly. Most other sectors are characterized by income elasticities of about one or greater than one, and therefore have higher growth rates.3 Even for industries that do not sell directly to households, income elasticities are important because the demand for their products depends ultimately to a large extent on consumer demand for final products.4 2. Price elasticities of demand are defined in much the same way as income elasticities. They are important because over time the prices charged by different industries do not change at the same rate: Some products tend to become relatively cheaper, others more expensive. The relative price of household durables,


173

for instance, has declined over time, whereas health care has become relatively more expensive. The principal reason for these changes in relative prices is differential growth in productivity, a measure of the efficiency with which an industry converts its inputs (especially labor) into outputs. Thus the communications sector, which consists chiefly of the telephone industry, has had a high growth rate of productivity and this has made telephone service progressively cheaper. According to econometric studies, the price elasticity of telephone demand is significantly less than zero, so households and businesses have responded to lower prices by increasing their consumption. The opposite, needless to say, has occurred in industries with low productivity growth, though it should be borne in mind that the effects of unfavorable price trends may sometimes be offset by high income elasticities (and conversely).5 For industries with a low price elasticity of demand, or with near-average productivity growth, the effects described in this paragraph are unimportant. 3. Changes in international competitiveness are important for some sectors, particularly manufacturing and mining. The preceding paragraphs deal with domestic demand, some of which can be satisfied by imports. Similarly, foreign demand can be satisfied by exports from the United States. International competitiveness is determined largely by production costs here and abroad and by exchange rates; in addition, there are barriers to trade of various kinds. Rapid productivity growth in Japan and certain newly industrialized countries has made them more competitive in the U.S. market; on the other hand, the demand for American exports has benefited from growth in foreign incomes. As to exchange rates, the high value of the dollar in terms of other currencies that prevailed in the early 1980s stimulated our imports and hampered our exports. The subsequent weakening of the dollar has had the opposite effect, but the United States remains a net importer. These differences in industry growth rates, relative prices and international competitiveness, in turn, feed through into growth in profits and dividends for firms operating in each sector (see Table 7.2). The main defect of Tables 7.1 and 7.2 is that the major sectors it covers are too broad for security analysis. Its main purpose is to illustrate some important general principles of sectoral growth and to introduce a long-term perspective. We now proceed to the next level of detail, the major industry.6 In line with the orientation of this book, we focus on dividends. In Chapter 6 it was shown that over time aggregate dividends have been a roughly constant fraction of aggregate National Income, and by and large this remains true when the economy is divided into major sectors. Although the available data do not permit us to verify this for finer breakdowns, it seems plausible that this approximate constancy also holds for major industries. If so, the long-run growth of dividends in these industry is largely determined by the same factors discussed in connection with Table 7.1. From Table 7.3 it appears that the industries with the slowest dividend

174

SECURITY ANALYSIS

Table 7.2 Growth Rates of Corporate Profits and Dividends by Sector, 1948-1989 Profits after Tax Sector a

All sectors Domestic sectors agriculture, forestry, and fisheries mining construction durable manufacturing nondurable manufacturing transportation communications electric, gas, and sanitary wholesale trade retail trade finance, insurance, and real estate services

Net Dividends

Mean

S.D.

Mean

S.D.

.049 .042 .067 -.007 .075 .038 .043 .028 .091 .059 .050 .050

.146 .164

.068 .067 .049 .069 .070 .058 .067 .054 .100 .085 .071 .057 .049 .094

.050 .060 .460 [c] .256 .145

[b]

.096

[c] [c] .233

[c]

.327 [c] .113 .195 .241 .174 [c] .187

[c] .116 .051 .063 .099 .094

[c]

.184

a

Mean annual change in the logarithm of each sector's contribution to National Income. Standard deviation of the logarithmic changes. c Without capital consumption adjustment (see Chapter 2); includes factor payments to and from the Rest of the World, which are excluded from the other items. b

Source: Calculated from NIPA table 6.03B using diskettes from Bureau of Economic Analysis.

growth were textiles and steel. These two industries were adversely affected by competition from imports, which in the case of steel was both caused and aggravated by low productivity growth. High dividend growth can be observed in the telephone and airline industries, both of which had a high growth rate of productivity and also benefited from favorable income elasticities.7 A comparison of the airlines and the railroads suggests that some of the growth of the former was at the expense of the latter. Other industries with above-average dividend growth were electric and gas utilities and commercial banking. In interpreting the table the following points should be borne in mind: 1. The underlying data from the National Accounts are industry totals; they are not expressed per share and have not been adjusted for inflation.8 2. These data are "net," which means that the dividends received by the firms in an industry have been subtracted from the dividends paid by those firms. Industries such as life insurance normally receive more dividends from their investments than they pay to their stockholders. For such industries, none of which are included in Table 7.3, net dividends are normally negative. This "netting" of dividends serves to avoid double counting. 3. Since the Rest of the World is considered a separate sector, industries with large international operations—oil and motor vehicles are conspicuous examples—may at times take in more dividends from abroad than

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Table 7.3 Growth and Variability of Total Net Dividends in Selected Industries, 1948-1987

Logarithmic Growth Ratea

Standard Deviation*

Iron and steel Nonelectrical machinery Electrical machinery Food processing Textiles Pulp and paper Printing and publishing Chemicals Railroads Airlinesc Telephone and telegraph Electric and gas utilities Retail trade Commercial banking

0.021 0.051 0.078 0.062 0.009

0.307 0.135 0.228 0.131 0.251

0.054 0.073 0.077 0.036 0.091 0.101 0.085 0.057 0.080

0.108 0.193 0.162 0.167 0.403 0.050 0.063 0.094 0.118

ALL DOMESTIC INDUSTRIESa

0.067

0.060

Industry

a

Mean annual change in the logarithm of dividends.

b

Standard deviation of the changes in log(dividend). 1950-1987.

c

d

Excluding dividends received from or paid to the Rest of the World.

Source: Calculated from NIPA table 6.22b using diskettes from the Bureau of Economic Analysis.

they pay to domestic stockholders. Their net dividends will then be negative for some years, and they had to be excluded from the table. 4. As pointed out earlier, there are millions of corporations in the United States, of which only a small fraction are listed on stock exchanges or traded with any frequency over the counter. All these corporations, whether listed or not, are covered by the National Accounts. Industries believed to consist mostly of unlisted companies (particularly in the services, in construction, in real estate, and in wholesale trade) do not appear in Table 7.3. 5. The long-term growth rates shown in Tables 7.1, 7.2, and 7.3 may mask significant changes in trend over shorter intervals. 7.2.3 International and Regional Growth A corporation's performance and prospects depend not only on the industry (or industries) in which it operates but also on other factors, not all of them quantifiable. Here we digress briefly from industry aspects to deal with geographical factors, both international and regional.

176

SECURITY ANALYSIS

Table 7.4 Growth Rate of Real GDP % per year, 1974-1993 ADVANCED INDUSTRIAL COUNTRIESa

United States Canada Europe* Japan DEVELOPING COUNTRIES

East Asia South Asia Latin America Eastern Europe and former Soviet Union Sub-Saharan African Middle East and North Africa

2.9 2.5 2.7 2.1 3.8 3.0 7.5 4.8 2.6 1.0 2.0 1.2

a

Includes countries not shown separately. OECD members only. Note: Regional data are available in great detail from the Bureau of Economic Analysis (U.S. Department of Commerce), but we cannot summarize them here. Suffice it to say that regional growth trends in the U.S. are somewhat cyclical. Sometimes one region does best for a number of years, sometimes another. Population movements, generally toward the South and the West, appear to be significant in explaining regional growth. b

Source: For industrial countries: Organization for Economic Co-operation and Development (OECD); for developing countries: World Bank.

Most large U.S. corporations have international operations and/or investments in foreign affiliates; they may also export some of their domestic production, as do many smaller firms. The same applies, mutatis mutandem, to enterprises headquartered abroad. It is therefore important to all such firms how other parts of the world are doing. The growth rates shown in Table 7.4 are the most useful summary of general economic performance.9 Table 7.4 only calls for a few comments. During the two decades covered, growth in the industrial nations was fairly uniform; it was lowest in Europe and highest in Japan. Actually Japan's growth rate was very high during the second quarter of the twentieth century, but it slowed markedly thereafter and has not yet recovered. There is much more variation among the developing areas in the bottom half of the table. East Asia, helped by strong growth in mainland China, South Korea, and Taiwan, stands out; South Asia also grew strongly. By contrast, growth in the former Soviet Union and its satellites was close to zero. These countries, now independent, are still in a difficult transition to a freer economic system. Russia's growth rate was still negative in 1994-1995, but other nations in Eastern Europe appear to have turned the corner.


177

Regional growth rates within the United States are important to firms that do not operate nationwide. Although a movement toward greater concentration is now in progress, the majority of American banks operate only regionally or within one state. It will be many years (if ever) before the American banking system is dominated by a few nationwide banks, as has long been the case in other industrial countries. Other regionally specialized sectors include retail chains, home builders, and health maintenance organizations. To all of these regional growth is important. 7.2.4 Industry Structure

We now return to the discussion of industry aspects. One of the most influential notions of industrial organization is the "structure-conduct-performance" framework, which postulates that the average performance (including profitability) of firms within an industry will be systematically related to the structure of the industry. Here the term "structure" refers to the state of competition within the industry, as manifested by such factors as the concentration of suppliers or the barriers to entry. These relationships will reflect both direct effects of industry structure on profitability as well as indirect effects, through which structure influences the conduct of the firms (for instance, whether they emphasize competition through price, through new products or through advertising). If, in fact, some competitive environments offer higher profit potential for well-run firms than others, security analysis could benefit from distinguishing between favorable and less favorable industry structures in valuing the securities issued by a firm. It could also usefully deploy information about changes in industry structure to predict how the profitability and cash flow of firms in an industry might evolve in the future. There is a considerable body of evidence to suggest that these industry structure effects are important. In studies by the Federal Trade Commission, the average profitability of some industries like breakfast cereals and Pharmaceuticals are found to be consistently high. Others, such as children's outerwear and metal cans, have consistently been among the least profitable industries. In other cases, such as air transport, average profitability has seen major shifts following changes in industry structure when deregulation caused entry of new competitors followed by increasing concentration. Porter (1980) has summarized the basic forces that should be considered as part of an assessment of a firm's long-term competitive position using the framework in Figure 7.1. These five competitive forces—threat of entry, threat of substitution by alternative products, bargaining power of buyers on one hand, and suppliers on the other, and rivalry among existing competitors—determine the long-term profitability of a firm and hence its value. By understanding these forces, the influence of transient influences—such as the current stage of the business cycle, temporary shortages of material or labor disputes, and short-lived spurts in product demand—can be seen in their proper context. The dangerous

178

SECURITY ANALYSIS

Figure 7.1

The "five forces framework." Source: Based on M. E. Porter, Competitive Strategy, Free Press, 1980.

temptation to project recent growth and profit performance linearly into the future can be avoided because the likely responses of potential entrants, buyers, suppliers, and competitors, all of which can greatly alter any profit and growth scenario, are always considered early in the analysis (Hay and Williamson, 1991). While it is not possible here to go into the details of industry and competitive analysis, it is worthwhile to expand briefly on the five forces just listed to see how these concepts might be used in security analysis. In Section 7.3 we discuss how an understanding of the industry structure might be merged with analysis of published accounts in the course of valuing a security. 1. The threat of entry to a firm's industry is a particularly important determinant of its future profitability. Entry, whether by new firms or through diversification or acquisition of existing ones, tends to force reductions in an existing company's market share, often causing price reductions and increases in the costs of raw materials or labor in the process. The valuation of Apple Computer, with its early dominance of the personal computer market, was a classic example of the need to take entry into account. Allowing for the impact of the threat of entry on the value of a security involves an assessment of both how easy it is for new competitors to enter (i.e., the height of barriers to entry) and the likely reaction of the firm and existing competitors should entry occur. The most important barriers to entry that might protect a firm's existing high profit stream into the future are: • Economies of scale, which may mean that new entrants face higher costs compared with existing firms with large production • Product differentiation in the form of brand recognition, loyalty of consumers or distributors, all of which may take entrants a great deal of time or costly advertising to break down • Proprietary technology or product design. Other barriers can arise from high costs of switching from one supplier to another (e.g., retooling or resistance from operating staff), access to distribution


179

channels (thus unproven brands often have difficulty competing for shelf space in retail stores), access to the best locations or raw materials if these are already controlled by existing firms, and government restrictions on new entry through licensing laws. 2. The pressure from substitute products may also have a significant influence on future profitability. If certain substitutes will improve their future price or performance in the same function as a firm's product, its past record will be a poor guide to the long-term value of its shares. Such improvements in the competitiveness of substitutes may come from technological change, but this is far from the only source. Major entry into the industry producing a substitute, for example, may cause a large fall in price and hence encourage many customers to switch towards it at the expense of the firm under review. The introduction of hand-held electronic calculators, for instance, doomed the slide-rule industry to extinction. This threat of substitution underlines the need for security analysts to understand not only the industry in which a firm operates but also industries producing functional substitutes for its products, some of which may not pose an immediately obvious threat. 3. The next force to be considered consists of possible changes in the bargaining power of buyers of the firm's products. Such factors as exit, mergers or acquisitions, or the emergence of a few dominant producers may lead to concentration of power into a smaller number of buyers (each purchasing substantial volumes compared with a firm's total sales) and result in a long-term decline in price. It may also lead to higher production costs as buyers use their greater bargaining power to pressure for higher quality or more support services. Such buyer pressure will have particularly adverse effects when the buyers can easily switch to another supplier, while the costs borne by the seller in adjusting to a different set of customers are high. 4. Possible future changes in the bargaining power of suppliers need to be taken into account. As in the case of buyers, developments that concentrate power in the hands of a small number of suppliers are likely to adversely affect a firm's profitability as suppliers demand a bigger share of the overall margin in the chain between final product price and the costs of producing basic raw materials. 5. Finally, the analyst must consider possible future changes in the pattern of rivalry between existing competitors. The current profitability of a firm, in part, reflects the behavior of its current competitors. In many industries with relatively small numbers of participants, there exists an "equilibrium" in which firms, recognizing their mutual interdependence, avoid actions (such as "price wars") that would lead to a general reduction in profit margins. Several kinds of developments may upset this cozy equilibrium. A decline in industry growth may cause competitors to scramble for share and impair unit margins. Industries where there is a high component of fixed costs and/or substantial barriers to exit (e.g., specialized equipment with low resale value) are especially prone to this scenario; airlines are a case in point. Conversely, in industries where capacity must, by technical necessity, be added in large increments, future growth may

180

SECURITY ANALYSIS

lead to recurring periods of overcapacity and price warfare. Entry of new firms, increases in imports, or takeovers may also disturb the competitive equilibrium in an industry and leave margins permanently impaired even when the industry settles down again (Williamson and Hu, 1994). Likewise, technological change can be a source of changed behavior of competitors with strong impacts on firm profitability. In predicting the implications of these changes in rivalry, an analyst needs to know whether the growth rates, pricing, and marketing strategies of the main competitors in the industry are consistent with trends in the market as a whole. In other words, he or she must ask, "Is each firm's planned growth consistent with the growth rate of demand across the market as a whole, or will it set off a struggle for market share?"10 7.2.5 Firm-Specific Factors

So far we have considered a framework for analyzing the impact of industry structure and growth on the profitability of firms, and hence the value of their securities. However, it is not generally true that "industry is destiny." Some firms manage to report high profits in industries that look unattractive in respect of structure or growth. A good example is the Crown Cork & Seal company, which achieved profitability of three or four times the average of its industry (metal cans) over a long period. Other firms produce poor profits despite operating in industries where the profit potential should be high given favorable industry structure and growth rate. Probably the most extensive analysis of whether there are persistent differences between the profitability of individual firms and the average profitability of their respective industries was undertaken in a comparative study spanning the mid-1960s to the early 1980s for samples of firms in Britain, Canada, France, Germany, Japan, and the United States (Mueller, 1990). The first important finding of this study was that the average coefficient of variation of firm profitability (measured by accounting return on assets) within an industry was around 0.5. In other words, the dispersion of return across individual firms in an industry was quite substantial with a standard deviation close to one half of the mean. Interestingly, this dispersion became wider in years with low profitability for most Canadian, French, German, and Japanese industries. This suggests that in these countries firms differed substantially in the extent to which they were affected by bad times in an industry. In Britain and the United States, the dispersion narrowed in low profit years, suggesting that the differences between firms were more closely related to their ability to take advantage of buoyant periods. A second key result was that there were persistent differences in the profitability of individual firms within an industry over long periods of time. There was a tendency for the competitive dynamics in a market to drive the profitability of individual firms up or down toward some long-run industry average determined by the structural features of the industry described above. However, this


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process was found to be both slow and incomplete. Therefore the most profitable firms in the initial period tended to have above-average profitability throughout the period. The opposite was true for the least profitable firms. Moreover, the variation between firms often dwarfed the variation in profits over time exhibited by the average firm in an industry. These results suggest that profitability differences between firms are based on structural factors associated with a firm's tangible and intangible assets and the barriers to imitation that protect its strategy from erosion by "copy cat" competitors.11 Security analysis, therefore, must not only concern itself with industry differences, but also try to understand the aspects of a firm's strategy and asset base, which help it achieve sustainable advantage over its competitors. While definition of a firm's strategy involves many complex factors, higher profit must ultimately stem from either lower costs or higher prices (or for outstanding firms, perhaps both). This fact has led analysts to identify three basic sources of potential long-run advantage: cost advantages, differentiation, and focus. Cost advantages, as the phrase suggests, are aspects of a firm's strategy that help it achieve consistently lower final product costs than its competitors. This position might be achieved by building large-scale plants, by pursuing volume more aggressively (which has led to greater accumulated experience than smaller competitors), by developing proprietary systems for tight cost control and inventory minimization, by using cash flow to continually invest in efficient state of the art equipment, by spreading fixed costs by sharing facilities or marketing distribution systems with other products, and so on. Even if rivalry drives prices down to competitors' break-even levels, a firm with overall cost leadership can still make good profits. Its lower costs are a source of extra profit margin at any given industry price. Similarly, it still has room for profits even if the force of substitute products or powerful buyers squeezes competitors to the brink of bankruptcy. Differentiation involves developing some aspect of a product in a way that makes the firm's offering unique in a way that is valued by customers. This uniqueness may be achieved by different physical or performance characteristics of the product (its "quality"), by the way it is marketed or distributed (often termed the "informational" characteristics of the product). The use of brand names and of after-sales service may foster customer loyalty. Innovative product or process technology may help a firm maintain differentiation of its product offering against imitation by competitors. Differentiation of a type valued by the customer results in a price premium that, depending on the costs of differentiating the product, can enhance the firm's margins compared with competitors. Developing customer loyalty helps shelter the firm if substitutes become cheaper. Since the buyer of a differentiated product loses something by shifting to another supplier, differentiation will often constrain buyer power in forcing lower margins. Thus the firm with a wellconceived differentiation strategy will have advantages in competitive rivalry. Focus is the third general source of advantage. A firm may gain advantages

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SECURITY ANALYSIS

over its competitors by concentrating on a particular customer group, a specialist item within a product line, or a particular geographic area. The advantages may stem from cost leadership in serving that focused segment (for instance, cost advantages in distributing to concentrations of customers in a small area), or from differentiation in the eyes of that segment (as with salespeople who have special knowledge of the insurance needs of doctors and dentists).12 All three sources of advantage are subject to erosion over time. Technological change may eliminate cost leadership, or a competitor may build a largerscale plant with a new, even lower cost structure. Competitors may imitate the characteristics, distribution methods, or product image that previously differentiated a product.13 Market segments on which a focused strategy was built may be invaded by competitors using national advertising or introducing multipurpose products. Having identified the sources of a firm's competitive advantage, the security analyst must therefore give careful consideration to the robustness or "defensibility" of that strategy against future moves by competitors, buyers, suppliers, or producers of substitutes. He or she must ask, "What are the future weak points of the strategy?" The answer to this question will determine the strength of tomorrow's cash flows and hence the current value of the firm's stock. In today's uncertain economic environment, this type of strategic assessment is one of the prerequisites for informed judgments about a firm's future growth in sales, profit performance, and need for additional capital. The next challenge for the analyst is to express those judgments in a quantitative way that can be meaningfully compared with the current stock price.

7.3 THE ROLE OF FINANCIAL STATEMENT ANALYSIS

Financial statement analysis has two main functions in the more general task of security analysis: • To measure the past and present performance of a firm's strategy • To provide a framework for quantifying judgements about the future performance of a firm's strategy and the risks associated with it The principal ingredients of financial statement analysis have already been described in Chapter 1. They are the firm's balance sheet, its income statement, and its cash flow statement.14 These are normally published each year in the report to the firm's shareholders, which may also be a useful source of information on management's view of the company's strategy. Greater financial detail is available in the annual 10-K reports, which public corporations are required to file with the Securities and Exchange Commission. Updated information may be obtained from the quarterly version of documents filed with the SEC (Form 10-Q).15 In using these statements to assess the past performance of a firm's strategy,

THE ROLE OF FINANCIAL STATEMENT ANALYSIS

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the analyst's main approach is to compute various ratios of the reported variables; the ratio of sales to total assets, sometimes called the "asset turn," is an example. Each ratio means little taken in isolation. Ratios are instructive only when compared with those of competitors or the ratios achieved by the firm in earlier time periods. In making these comparisons, great care must be taken to check the "notes to the accounts" for differences in the accounting conventions adopted that could distort the interpretation if not allowed for (for instance, straight line versus declining balance methods of depreciation).16 When a significant difference in a ratio is identified, the analyst must consider whether this results from different performance or a different choice of strategy. Since failure to make this distinction has been the cause of much erroneous analysis in the past, further elaboration is worthwhile. Take the example of two construction companies, DIY and AUO. On computing their "fixed asset turn" (sales/fixed assets), we find that DIY has a ratio of 1.5 compared with AUO at 3.0. Interpreting this difference as purely one of performance, we might conclude that DIY is plagued with low capacity utilization and idle fixed assets, whereas AUO uses its assets continuously to produce twice the revenue from every dollar of fixed assets on its books. Interpreting the difference as one of strategy choice, we might conclude that DIY owns all of the equipment used on a job. AUO, meanwhile, rents its equipment, employs subcontractors, and owns few fixed assets itself. Certainly, AUO (Always Use Outsiders) has a much higher asset turn, but much of its sales revenue is paid out to equipment owners and subcontractors. DIY (Do It Yourself) has less sales per dollar of fixed assets, but all of that sales revenue is available to cover its internal operations. The implications for the value of each firm's shares differ. If performance is measured by the fixed-assets turn, then AUO will be worth more until DIY gets management that attracts more sales or disposes of assets. If the difference actually reflects a strategic choice, the story could be the opposite. In profitable boom periods in construction, DIY has a guaranteed supply of equipment as a basis for accepting work and making profits. AUO may be left struggling to find subcontractors at high prices in a tight market, having to turn down work at the most profitable time. Provided the costs of holding assets in recessions are relatively low, DIY would then be the more valuable company. Likewise, changes in ratios over time for any one company may reflect trends in performance or shifts in strategy toward the market. We now briefly discuss some of the information about performance and strategy that might be gleaned from other key ratios. The first major set of ratios focuses on the income statement and attempts to picture the division of each dollar of sales revenue between raw materials costs, production operating expenses, and the return to providers of capital (comprising interest paid to debt holders and profits to shareholders). The gross margin (gross profit/net sales) can be used to provide information about both changes in demand and buyer power, and the degree to which a firm

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SECURITY ANALYSIS

is benefiting from a differentiation strategy. Comparison of the gross margin achieved by a firm over time could, for example, point to a decline in the funds available to meet profits and operating expenses, which may in turn signal the presence of intensified competition from substitutes, growing buyer power, and so on. By comparing gross margins across firms within an industry, meanwhile, it is possible to identify firms that are achieving higher price realization over their cost of raw materials by differentiating their product (e.g., by precision in production, by strong sales support, or by advertising). In order to get a fuller picture of the firm's strategy and performance, however, we must examine the net margin (net profit before interest and taxes/net sales) in conjunction with gross margin. In the cross section context, it helps us understand whether the differentiation adopted by individual firms is really profitable; in other words, whether or not the increase in gross margin achieved through differentiation outweighs the increase in operating expenses incurred in differentiating the product.17 A high gross margin and low net margin compared with competitors suggest the firm is engaged in unprofitable differentiation. The question then becomes whether this is an inherent problem in pursuing a strategy of differentiation or simply poor control over the expenses involved. A furniture company, for example, may differentiate its product by offering a wide choice of covering fabrics. If we observe a higher-than-average gross margin and a below average net margin, it may be because the price premium that consumers pay for this choice does not cover all the additional costs of carrying extra stock, disruptions to production flow involved in making to order, lower labor productivity with unfamiliar fabrics, and so on. On the other hand, it may reflect poor stock management and production scheduling compared with efficient methods. These alternative explanations have different implications for the fundamental value of the stock. If it is a basic flaw in the firm's whole approach to the market, hence costly and difficult to change, value will be lower than if the problem is one of management control (in which case the firm is probably a good candidate for takeover, replacement of management, and a substantial increase in value). The individual expense ratios (e.g., selling expenses/net sales) are useful in identifying which part of the company's operations are responsible for any problems in net margin observed. This could show up either as a trend for certain expenses to absorb a higher proportion of sales revenue over time or as an expense ratio that is out of line with competitors. Again, we must ask whether such differences in expense ratios make sense in terms of profitable differences in the firm's strategy or reflect poor performance. A second set of ratios giving insight into the operations of the firm are those relating income statement variables to the balance sheet. We have already discussed one of these: the fixed asset turn (net sales/fixed assets). Others include inventory turnover (cost of goods sold/average inventory), accounts receivable


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turnover (net credit sales/average accounts receivable outstanding), and working capital turnover (net sales/net working capital). Both inventory turnover and accounts receivable turnover, viewed over time and across competitors, offer a way to judge the company's performance in respect to inventory control and debtor collection. As a general rule, high ratios are desirable. As always, however, allowance must be made for any differences in strategy that may underlie them, the two furniture manufacturers being a case in point. A third important group of ratios are helpful in forming a judgment as to the firm's financial (or bankruptcy) risk. These include the times interest earned ratio (net profit before interest and taxes/annual interest charges), the fixed financial charges ratio (net profit before interest and taxes/annual fixed financial charges), the debt-equity or "leverage" ratio (current and long term liabilities/ total liabilities and shareholders funds), and the cashflow ratio (total debt/cash surplus on operations after tax per annum). The times interest earned ratio, sometimes termed interest cover, is a measure of how much the net operating profit of the firm could fall before it would be unable to meet its interest commitments. Clearly, the closer the ratio falls toward 1.0, the smaller the reduction in earnings the firm can tolerate before serious financial problems arise, and thus the greater the risk. The fixed financial charges ratio is an analogous extension. It recognizes that there may be other fixed financial claims against a firm's income that could result in bankruptcy if not met. The most important of these is lease commitments, which are therefore added into the denominator. The debt/equity or leverage ratio is probably the most widely used of all measures of financial risk. Provided the liquidation value of the company's assets is correctly reflected in the accounts, it reflects the percentage loss in asset value (either as the result of future trading losses or extraordinary items such as the writeoff of a large bad debt) that the company could buffer with its equity before the creditors began to lose their capital. If, for example, a firm has $100 million of assets and a leverage ratio of 0.5, it could afford to take losses equal to an average of 50% on all assets before the creditors would face a serious loss of principal. This may seem unlikely, but we should recall that a number of large banks—with heavy loan exposure in real estate and developing countries—and high leverage have recently faced the prospect of almost completely wiping out their total equity base with loan writeoffs. In the early 1980s, the Chrysler Corporation had to be "rescued" from a similar fate, in this case because of trading losses. In addition to protecting their capital, another concern of creditors is the liquidity of a firm. The cash flow ratio is one indicator. When a firm has a low ratio of short-term debt to cash surplus on operations, it will have better options for repaying some of these loans when credit markets become very tight, thus presenting difficulties in rollover or refinancing of loans during the squeeze. From a long-term perspective, the ratio of total debt to cash surplus on operations is used as an indicator of the company's ability to repay its existing loans

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SECURITY ANALYSIS

without recourse to refinancing, allowing future borrowing to be directed toward new investment and growth. Before leaving the topic of ratio analysis, we should mention two other measures that are in common use but have some significant problems: the current ratio, which is also known as the working capital ratio (current assets/current liabilities), and the quick asset or "acid test" ratio (current assets less inventories/current liabilities). These ratios purport to show a company's ability to repay its short-term debts. To answer this question, we really want to know whether cash on hand plus expected inflow of cash from sales, collection of receivables, and rundown of inventories will exceed the forecast need for cash to repay maturing liabilities, make new investments to maintain production, and pay ongoing expenses. Instead, these ratios tell us how big the stock of current assets is relative to the existing current liabilities. That is only one small part, the base point in a sense, of understanding the firm's future cash position. Moreover, the working capital ratio could be high, for example, because the firm's inventory is poorly managed so that current assets are excessive. These examples illustrate two problems with ratio analysis in general: They are really measures of past strategy and performance when what we need is an explicit forecast of the future; and they fail to highlight the interrelationships between the firm's strategy, operations, and financing.18 Using ratios in a way that helps to overcome these deficiencies is the subject of the next two sections. 7.3.1 The Adjustment Process of Financial Ratios

The financial ratios discussed above can be categorized into two broad types. First, there are those that relate various assets and liabilities in the firm's balance sheet to each other. These represent the inputs that the firm uses to generate its income. Economic theory tells us there is some optimal combination of these inputs that will minimize the firm's costs.19 This means each firm will have some optimal structure of assets and liabilities that can be reflected in the ratio of balance sheet components. At any time a firm's asset-liability structure is likely to have been displaced from this optimum by random or short-term shocks, such as an increase in inventory following an unexpected downturn in demand. The optimal structure may also be a "moving target" as changes in relative factor costs or technological improvements, for example, change the optimal mix of assets and liabilities. Management will therefore be continually adjusting these balance sheet ratios to move toward the optimal structure. Some of the ratios we have just discussed can be readjusted quickly. The current ratio, the quick ratio, and the inventory turnover can probably be altered in a matter of months, certainly within a few years. Other ratios involving buildings, plant and equipment represented by fixed assets, and long-term liabilities and equity can be expensive to change quickly and frequently. Major changes in


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the debt/equity ratio, for example, are usually achieved through lengthy and infrequent processes of issuing new bonds or equity or by gradually reducing the dividend payout ratio so as to build up shareholders' equity through retained earnings. Share repurchase and redemption of bonds are also methods of adjusting the debt/equity ratio. The second broad group of ratios, primarily those derived from the firm's income statement such as return on sales, are a reflection of management initiatives to improve performance, combined with the competitive dynamics and structural changes in the firm's product markets. Here there is not really "target ratios" as such but a competitive equilibrium level for each ratio given the structure of the industry. Just how fast these ratios move toward equilibrium depends on the strength of market forces operating in the industry. At the same time, many management actions are aimed at improving their firm's position relative to the long run industry average, interrupting convergence to the competitive equilibrium. As shown in Section 7.2.5, some firms are quite successful in maintaining aboveaverage performance ratios compared with their competitors over long periods, while others are chronically below average. The question for the security analyst, then, is, How fast will an individual firm be drawn to the industry average level by market forces? The answer will depend importantly on the nature of these advantages and how easily they can be replicated by competitors. Peles and Schneller (1989) examined the adjustment process of six financial ratios for 635 U.S. corporations based on annual changes over the period 19611980. For all of the ratios they found a negative serial correlation of the annual changes; in other words, an increase or series of increases in a ratio in one year was more likely to be followed by a decrease in the following year or series of decreases than further increases. This result is important for security analysts seeking to forecast changes in financial ratios. As expected, the speed of adjustment varied significantly between different ratios. Estimates of the adjustment speeds are shown in Table 7.5. The results suggest that approximately 40% of disequilibrium in "short-term" ratios like the current ratio, the quick ratio, and the inventory turnover is eliminated within one year. By contrast, the debt/equity ratio, return on assets, and the total asset Table 7.5 Adjustment of Financial Ratios Ratio

Adjustment per Annum (%)

Current ratio Quick ratio Inventory turnover Debt/equity Total asset turnover Return on assets Source: Peles and Schneller (1989).

40 36 40 12 19 11

Duration of Adjustment (Years)

2.5 2.75

2.5 8.5

5.25 8.75

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SECURITY ANALYSIS

turnover exhibited much slower rates of adjustment of only 12% per year for the first two and 19% per year for asset turnover. The analyst can use these results as a guide to forecasting how fast management will realistically be able to eliminate an unwanted change in its financial structure or how long a significant change in performance might last. The results imply nothing about the level of the equilibrium or target to which the ratio might converge. Early work in this area suggested that the industry average might be used as a measure of the equilibrium or target. Figure 7.2 gives an indication of the differences in the debt/equity ratio across industries and across time. Care must be used in employing these industry benchmarks. While a potentially useful guide, recent work (Foster 1986) suggests that the links between the industry average and adjustments in financial ratios by individual firms are not always tight. This finding underlines the need to take into account the possibility that particular firms may be able to maintain persistently different ratios from the industry average because of differences in their market strategy. For example, if a firm differentiates its offering on the basis of fast response to its customers, even at the expense of excess capacity and high inventory, then it may maintain persistently lower asset turns than its competitors. It will still be profitable if customers pay a compensating price premium for this high level of service. 7.3.2 Pro Forma Income and Cash Flow

We began this chapter with the basic proposition that valuing a security involves estimating the future cash flows it will provide and discounting these by an ap-

Figure 7.2 Industry average debt-equity ratios. Source: Data from the Brookings Institution.

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propriate rate to account for the greater value of money received sooner rather than later, and the risk that the cash flows might vary substantially from our base estimate. The cash flow pro forma set out in Table 7.6 offers a framework for deriving estimates of the future cash flows by combining data from the last available income statement and balance sheet with an assessment of the growth and financial ratios likely to be achieved in the future. It is in the process of implementing this approach that the streams of strategic and financial analysis come together. In deciding how the ratios used in the pro forma, such as gross margin or fixed asset turnover, will change in the future, the analyst must draw on a strategic understanding of the forces of change at work in the firm's markets and its strengths and weaknesses relative to competitors. Likely changes in each of Porter's five forces bearing on the firm must be assessed and their impact on each individual ratio identified. The next step is to go through the calculations laid out in Table 7.6, using depreciation and interest expenses based on the fixed assets and outstanding debt appearing in the latest balance sheet and current sales from the income statement. This computation results in an estimate of the net cash flow generated or required by the firm's operations during the first year (in the final row). This net cash flow from operations can then be used to derive the debt Table 7.6 Cash Flow Pro Forma Item

Computation

Future Sales

Current Sales x (1 + Expected Growth)

Gross Profit

Future Sales x Expected Gross Margin

Cash Flow from Direct Operations

Gross Profit — (Future Sales x 2 Nonfinancial Expense Ratios) — Interest on Existing Debt - Taxation Payable"

Increased Investment in Receivables Increased Investment in Inventories

(Future Sales x Expected Receivables Turnover) — Existing Receivables (Future Sales x Expected Inventory Turnover) - Existing Inventory

Increased Investment in Other Current Assets

(Future Sales x Expected Other Current Asset Turnover) - Existing Other Current Assets

Increased Investment in Fixed Assets

(Future Sales x Expected Fixed Asset Turnover) - Existing Fixed Assets

Cash Flow Generated or Required by Operations

Cash Flow from Direct Operations (Increased Investment in Receivables, Inventory, Other Current Assets and Fixed Assets)

"Nonfinancial ratios exclude interest and depreciation. Taxation Payable = (Cash Flow from Direct Operations — Depreciation) X Expected Effective Tax Rate.

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SECURITY ANALYSIS

outstanding by the end of year 1 and hence the interest expense for the following year. Likewise, the depreciation expense in year 2 can be computed from the increase in investment in fixed assets. Both of these calculations are shown in Table 7.7. With these new estimates of financing and depreciation expenses in hand, the computations set out in the cash flow pro forma (Table 7.6) can be repeated to derive the cash flow required or generated by operations in year 2, and so on. The spreadsheet software now widely available for microcomputers is well suited to this repetitive calculation. The resulting data series can be used both in a direct calculation of security value and to compute some of the basic indicators of bankruptcy risk. In applying the standard discounted present value formula, the first problem we face arises from the fact that the shares in firm are usually regarded as perpetual securities. We could thus go on computing the cash pro forma into the hereafter. One solution is to replace the annual cash flows beyond, say, 5 years with a single "terminal value" as follows:

where ECF(t) is the estimated cash flow in year t and ECT is the net annual cash flow in real terms beyond year 5. The assumption underlying this formula is that after year 5, ECT simply remains constant in perpetuity. Obviously some bias is introduced. Once we get far enough out into the future, however, the discounted Table 7.7

Recalculation of Interest and Depreciation

Item

Computation

Cash Flow Generated or Required by Operations

From Cash Flow Pro Forma

Dividend Payments

(Cash Flow from Direct Operations — Depreciation) x Dividend Payout Ratio

Net Cash Flow

Cash Flow Generated or Required by Operations — Dividend Payments

New Debt Outstanding

Existing Debt Outstanding - Net Cash Flow

Interest Expense in Year t+1

New Debt Outstanding x Average Interest Rate

Depreciation Expense in Year t + 1

(Existing Fixed Assets + Increased Investment in Fixed Assets) x Average Depreciation Ratea

a

For example, a rate of 0.1 for 10-year straight-line depreciation.


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present value of a dollar is so small that the resulting security value is not particularly sensitive to our assumptions and the bias they contain. The second problem is what discount rate to use. It should be the cost of equity capital to the firm; in other words, the return that will induce investors to include the firm's shares in their portfolio. We derived a formula for this figure in Chapter 5, which uses an estimate of the firm's systematic risk or beta as follows: r=Rf+ L(Rm— Rf), where is the firm's beta adjusted for its debt/ equity ratio, also known as leverage (hence the subscript L). Before applying this formula, however, the analyst needs to incorporate a judgment about how the firm's beta might change in the future. Again, this is where the strategic analysis of the five competitive forces acting on the firm and the strength and robustness of its competitive advantage enters into the calculation. For example, is the firm's strategy leading it to become more dependent on cyclical swings in growth of the national economy? If this were the case, we would expect its beta to increase. We now (at last!) have a valuation of the firm's shares that reflects both the likely evolution of its cash flows and its systematic risk. It remains, then, for us to make some assessment of the changes in its risk of bankruptcy. From the cash flow pro formas we can calculate the indicator ratios mentioned in Section 7.3, such as times interest earned, leverage, and the cash flow ratio. Sufficiently serious deterioration in these indicators of bankruptcy risk would necessitate a subjective downgrading of the earlier valuation. One method would be to add a further "bankruptcy risk premium" to the discount rate used in the valuation formula. 7.3.3 Caterpiller Inc.: A Security Analysis and Valuation Example

Caterpillar is the dominant American competitor in the worldwide earth-moving equipment industry, selling its products to construction, mining, oil, and forestry companies. Despite the cyclical nature of its markets it had operated for more than 50 years up to 1980 with only a single year of loss. That year was 1932, in the worst of the Great Depression. It built an exceptional market position, attaining a share of over 50% of the world market for earth-moving equipment. It maintained this position throughout the entire decade of the 1970s and was one of a handful of companies singled out for effective management by Peters and Waterman (1982) in their popular book In Search of Excellence. It has long been one of the largest net exporters in the United States, with total exports in 1992 amounting to $3.33 billion. During the 1980s, however, its performance became much less certain, as is evident from Figure 7.3. In the report to shareholders for 1990, the chairman stated: "Nineteen ninety was a disappointing year. Sales and revenues reached record levels, but profit was clearly unacceptable. Improving long-term profitability is an urgent priority, and as you'll read in this report, we're taking action

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Figure 7.3

Recent performance of Caterpillar Inc. Source: from the company's Annual Reports.

Calculated

to make Caterpillar a stronger competitor and better investment for stockholders." In the short term, the company went on to make losses in both 1991 and 1992. Fundamentally altering its costs and revenue streams has proved to be painful, but Caterpillar continues to adjust to the structural changes in its market and the increasing competitor strength that began to affect the firm in the early 1980s. In order to do so, it has invested more than $4.5 billion in fixed assets since 1986 as part of a program of factory modernization. In 1992 its operations generated $503 million of cash compared with $1 billion of cash needs. The valuation of its securities therefore represent a useful example of how industry, firm, and financial effects must be brought together in security analysis. In terms of the five forces discussed in Section 7.2.4, the earth-moving equipment business had a number of attractive structural features. The market is concentrated in the hands of eight players worldwide. Both buyers and dealers are much more fragmented than the equipment suppliers, reducing their bargaining power. Likewise, parts and raw materials are generally shared with other industries (such as truck and tractor production), so they tend to be available from a number of alternative suppliers. There are substantial barriers to entry because it is difficult for dealers to divert their sales attention from proven products, train their service engineers in a new product, and duplicate their inventory of spare parts for a new product with initially small market share. The major substitute for earth-moving equipment is additional labor, which is becoming increasing expensive in real terms throughout most of the world.


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On the downside, the cyclicality of the construction industry forces the earth-moving equipment producer to go through periods of excess capacity when demand falls off and suffer high costs of excess demand in boom periods. The growth in the industry is now modest in much of the developed world, with most of the growth confined to developing countries. Since labor is much cheaper there, the forces of substitution place greater limits on the prices of expensive equipment. The dealer networks of the major suppliers are less well developed in the third world, allowing better opportunities for smaller rivals or new entrants. Many of the projects are sponsored by governments who put the equipment out to competitive tender. These trends mean that the industry has become structurally less attractive since the early 1980s. Caterpillar had maintained above-average profitability compared with its industry by differentiating its product in terms of quality (low levels of breakdown) and high levels of service through an extensive dealer network that supplied maintenance and parts as well as sales information. The costs associated with breakdown are high for many customers. In the construction industry, for example, breakdown of earth-moving equipment can delay the whole schedule and leave expensive labor and materials idle while waiting for the basic work to be completed. Thus many customers were willing to pay a substantial price premium (around 15%) for high quality and service. Caterpillar used this premium to pay its dealers attractive margins, to hold excess capacity in production with which to respond to upswings in the construction cycle, to maintain high inventories of parts that enabled it to respond quickly to breakdowns and quality problems, and last but not least to provide its shareholders with attractive returns. Some of the competitors, notably Komatsu of Japan, had developed their product quality to close the gap with Caterpillar by the early 1980s. This competition reduced Caterpillar's ability to maintain a price premium and shifted the focus more onto competition on the basis of costs, a trend that was given further impetus by structural changes in the market. Komatsu intensified this pressure by developing ways of reducing inventory turn through modular designs, which reduced the number of different components, and employing "just-in-time" logistics systems. It also introduced more flexible manufacturing and supply chains to permit more variety to meet the precise specifications of different customers operating in different geographic environments and different user industries throughout the world. Komatsu also slowly built a substantial sales and service network. In Europe, meanwhile, mergers between French, German, and the subsidiaries of some American firms produced larger, more powerful competitors. Competitive pressure is therefore increasing in the face of an industry with modest long-term market growth. The shift in emphasis in the market towards cost competition, combined with higher levels of variety and flexibility that make a strategy based on a price premium less viable, present long-term problems for Caterpillar. The shift requires that margins be restored primarily through reduced costs and better inventory and asset turnover. Our cash flow pro forma must therefore be driven by

194

SECURITY ANALYSIS

these ratios, rather than significantly increased prices or sustained, rapid volume growth. The key questions are, How fast can Caterpillar adjust these ratios and how much cash will be required for investment in plant modernization and development of increased variety and new products? Figure 7.4 suggests that the management has been making some progress in improving the inventory and accounts receivable ratios in recent years. However, given the structural changes in the industry and competitive forces discussed above, it seems unlikely that accounts receivable turnover will return to the levels of the early 1980s. Continued improvements in logistics systems and modular redesign of products, on the other hand, should allow new levels of inventory turn to gradually be reached in the future. On these arguments, our pro forma calculations assume inventory turn will rise to 7 times over the next 5 years while receivables turnover will improve slightly to 5.5 times. Some of the other critical assumptions include an average growth in sales volumes of 3% per annum over the next 5 years, in line with projected growth in the world construction industry. We assume an average 3% per annum increase in average selling prices, just below more generally projected rates of inflation. This assumption reflects the difficulties of obtaining price increases in the more competitive market described above, and the continuing shift toward smaller machines in the product mix that has characterized demand in recent years. As indicated by management plans, we have factored in the continued need for investment in modernization at a rate close to $500 million per annum until after 1993, followed by continued investment of $300 million per annum subse-

Figure 7.4

Evolution of inventory and receivables ratios at Caterpillar Inc. Source: Calculated from the company's Annual Reports.

SHORTCUTS IN SECURITY VALUATION

195

quently. Finally, we have based our security analysis on the average margins on sales that characterized the industry in the late 1980s, rather than the higher levels that prevailed earlier. This decision reflects an assumption that the changes in the market and competitive forces we discussed above, as well as the reduced viability of maintaining a substantial price premium through a differentiation strategy, are structural shifts. Hence they are likely to characterize conditions in the future. Working through the pro formas set out in Tables 7.6 and 7.7, our estimates suggest that Caterpillar's ability to generate high returns for its shareholders will be held back by the interest and cash burdens associated with heavy investment in plant modernization and the need to finance rising accounts receivable, given the new realities of competition in the market. Expected improvements in inventory turnover, given the duration of adjustment, will be insufficient to offset the effects of this cash absorption. We cannot detail all of the other assumptions inherent in the pro forma cash flow calculations for the purposes of this example. Suffice it to say that the analyst must make estimates of future interest, inflation and tax rates by working through the macroeconomic considerations described in Chapter 2. The pro forma is a way of helping to sort out their implications for a particular firm given the structure of its assets, liabilities, revenues, and costs and the market pressures upon it. At the end of this process, we produced a series of forecasts of Caterpillar's cash flows from 1993 through 1998, after which we treated the cash stream as a perpetuity in the manner described in Section 7.3.2. When we discounted these cash flow forecasts back at an estimated cost of capital, we made allowance for the fact that Caterpillar's dependence on the construction industry tends to amplify the effects of the business cycle and give it a relatively high beta. The final result of this security analysis suggested an "inherent value" of one Caterpillar share of $58. Readers may be interested to note that during 1992 Caterpillar shares traded as high as 621/8and as low as 41 1/4. During 1993 Caterpillar's share price reached a high of 83, suggesting that the market had become much more optimistic than our security analysis would suggest was warranted. If our security analysis is at all accurate, the peak share price of $83 should have been vulnerable to disappointing earnings. This warning in fact proved correct, with Caterpillar's share price falling back to around 68 by late 1995—against the trend of a generally rising stock market.

7.4 SHORTCUTS IN SECURITY VALUATION

At this point some readers may ask, "Is all this complex analysis of financial statements, industry structure, and firm strategy really necessary; isn't there a simpler way?" They may have heard the claim that one simple rule of thumb can replace all of this security analysis: the price/earnings ratio (P/E). Perhaps

196

SECURITY ANALYSIS

less likely, they may have been impressed by the proponents of Tobin's q as a universal method of equity valuation. A brief discussion of these two concepts will be helpful. 7.4.1 Uses and Pitfalls of Price/Earnings Ratios

Price/earnings ratios are a simple way to express stock prices in terms of a common denominator. It is sometimes helpful to check whether a stock trading, say, $60 is in fact trading at a higher or lower premium than one priced at $40. If the first stock had earnings per share (EPS) of $6 and the second $4, then both would be trading at the same premium of 10 times earnings. If the latter stock had earnings of $8, however, its P/E multiple would be only 5. Why might an investor be willing to pay a premium of 10 times earnings for one stock and 5 times earnings for another, or 20 for yet another? To understand, this let us return to the dividend growth valuation model discussed at the end of Section 6.1:

where gd is the assumed growth rate of dividends and rs is the rate of return required by potential investors in this particular stock. Now the dividend in each period is equal to the earnings in each period multiplied by the dividend payout ratio:

where EPS(t) stands for earnings per share. If we are prepared to assume that the dividend payout ratio d(t) and the discount rate rs remain constant over time then earnings grow at the same constant rate gd as dividends, and the PVD formula also applies to earnings.20 It can then be seen the P/E ratio reflects a combination of simplifying assumptions about the dividend payout ratio, the expected rate of growth of earnings, and the discount rate (including some allowance for risk). This may look like a much simpler way to get an estimate of the "intrinsic" value of a stock. The problem is that those three variables—the anticipated future growth rate, the dividend payout ratio, and the discount rate—depend on all of the factors we have been discussing, including industry and firm effects and the firm's future investment needs. In a sense, the P/E ratio sweeps under the carpet many of the hypotheses one should make in order to analyze the appropriate value of a stock. In the 1960s, a number of investigators (e.g., Whitbeck and Kisor, 1963) estimated regression equations of the form: P/E = Y + 1g + 2d+ 3 , where g


197

was an estimate of future growth, d was an estimate of the dividend payout ratio, and was a measure of risk (namely the standard deviation). Once the equation was estimated, it was then used to estimate "intrinsic P/E ratios" for individual stocks. When the actual P/E was above the estimate, the stock was said to be good value. The problem with this should be clear: Deviations from the intrinsic P/E could represent either incorrect valuation by the market or failure of the assumptions of the simplified model to capture all of the significant influences on the fundamental value of the stock. Subsequent studies of the predictive power of these models suggested that the latter explanation (incorrect model specification) was usually the cause of what were, in fact, spurious deviations from the "true values". Although using P/E ratios in a less precise way, many commentators over the years have suggested that there is a "normal" of "sustainable" P/E for either the market as a whole or for particular stocks. Thus it was argued that in 1959 the S&P500 index, then equivalent to twenty times current earnings, was unsustainably high. During the period since World War II, actually, the P/E ratio corresponding to the S&P500 was highly variable, ranging from a low of 5.9 in 1949 to a high of 22.4 in 1961. Nor do its movements show a neat cyclical pattern: In fact, for about a dozen years after 1959, this P/E ratio stayed fairly close to 20 (using annual data), so anyone who thought it was too high in 1959 would have needed considerable patience to profit from his foreboding. After falling sharply in the 1970s to 7.4 in 1979, it recovered again and has recently fluctuated around 15. This suggests that the P/E responds to different information and expectations about growth and the appropriate discount rates. There is conceivably a "normal" level, determined by economic growth and real interest rates in the long run, but it would be difficult to determine. To find this "normal" level for individual equities would be even more difficult. While P/E ratios have some usefulness in "scaling" stocks of different unit values, they are not a substitute for careful security analysis based on an understanding of the industry and the firm's competitive advantages within it. Their most important application, perhaps, is in valuing the equities of firms that do not pay dividends but do have earnings—or at least prospective earnings.21 Such firms are usually fairly new and relatively small. If they have earnings at all, they often prefer to plow them back into the business, and this may indeed be the best use of these funds from the shareholders' point of view. In a new industry, such as biotechnology, there are typically many firms with no earnings at all. Their prospects have to be assessed on the basis of technological judgments concerning the merits of their production processes, and on economic judgments about the market for their products, assuming they can actually produce them. Any P/E ratio refers to the future and is of necessity highly conjectural. Some firms will have earnings, and in a new industry the P/ E ratios will usually be high, reflecting the supposed advantage of being ahead

198

SECURITY ANALYSIS

of the pack. Those firms can indeed be scaled by their P/E ratio, but one with a high ratio is not necessarily expensive; it may be that knowledgeable investors consider its prospects unusually promising. Even for those firms, consequently, the P/E ratio carries little information by itself. 7.4.2 Tobin's q as an Alternative Approach to Securities Valuation

While the P/E ratio focuses on the profit-and-loss statement of a corporation, Tobin's q (already discussed in Section 6.2 with special reference to the aggregate of all U.S. corporations) looks at its balance sheet. As we shall show, this is not the whole story, but it is a good starting point. When we state that the value of a firm, and hence the price of its equity, is the discounted value of future dividends, it is sometimes easy to forget that any business is not a "bundle of money" but a bundle of real assets, some tangible, some intangible. If you were to ask most laymen why a firm was worth something, they would probably point to the collection of plants, distribution centers, brand names, and teams of skilled individuals as the source of intrinsic value. We should therefore have something to say about how this complex collection of assets is reflected in the price of the securities that represent claims upon it. Suppose that a new company is set up with $1 million of equity capital. It then uses this money to construct a building on a new industrial site around which there is plenty of vacant land. What would the company—call it Specbuild Inc.—then be worth? A prospective buyer for this company might be another business wishing to move into expanded premises identical to this new building. They would have at least two alternatives. One would be to buy Specbuild Inc. lock, stock, and barrel. An alternative would be to build an exact replica on the vacant land next door. Leaving aside any differences in risk and the cost of renting other premises during construction, the value of Specbuild would therefore be equal to the replacement cost of its only asset, the building. The buyer would not want to pay more than the replacement cost, since it could avoid the premium simply by replicating the building. One way of expressing this would be to calculate the ratio of the market value of an asset (MV) to its replacement cost (RC). This is the ratio called q by Tobin (1958). Suppose you own one of the 1 million shares in Specbuild; how much would your share be worth? We could write the share price (PS) as: PS = MV/(1m) = (MV/RC)(RC/1m) = q(RC/1m), where "1m" is 1 million. If Specbuild were inexperienced in the building trade and so wasted much of the materials in scrap and made poor bargains with their contractors, it may have cost them $1 million to construct a building that a more efficient company could replicate next door for only $750,000. In this case q would be 0.75 and your share would be worth 75 cents. If, on the other hand, Specbuild were efficient builders and the city government subsequently intro-


199

duced a new flat rate tax of $500,000 on all new construction, the replacement cost might rise to $1.5 million, in which case your share would be worth $1.50. More generally, this model shows how inflation in the replacement cost will increase the value of assets that are easily replicated. Whenever there is little difference between buying an existing asset or replicating it with a new one, q will remain close to 1. This is because as soon as the market value rises relative to the replacement cost, suppliers will replicate the asset, increasing the quantity available and driving the market value back into line with the replacement cost. As the time lags involved in replication increase, temporary shortages may push q well above 1. Potential buyers may be willing to pay more for the building than its replacement cost now, so as to expand their business operations immediately, rather than wait for a new one to be constructed. Clearly this would be only a temporary phenomenon. Under what circumstances might the market value stay above the replacement cost (q> 1) for a long period of time? Instead of a building, consider the problem of replicating a different kind of asset bundle, say the IBM company. Although a Herculean task, you could attempt to replicate all of IBM's tangible assets: its factories, its research laboratories, its inventories, and so on. All of this would have some total "replacement cost." At this point, your IBM look-alike would only be worth the replacement cost of all these tangibles; q would still remain at 1. If, however, you were able to use the assets in your IBM look-alike to generate profits above your cost of capital, then this bundle of assets you put together would be much more attractive to investors and the market value would rise so that q > 1. Seeing a chance for capital gain by forming a bundle of assets, new entrants would spawn more IBM clones. The resulting competition in the computer market would drive your profits down, causing the market value of your company to fall back toward its replacement cost. Yet the real IBM did for many years sustain a market value that was probably a good deal higher than the replacement cost of its tangible assets.22 One important reason was its capacity to generate profits from its strong brand recognition, customer loyalty, and well-focused R&D, not to mention the collective know-how of its employees. By managing this complex portfolio of tangible and intangible assets in concert over a long period of time, moreover, IBM accumulated great experience in creating value for its customers and shareholders. What makes a company really valuable is the ability to construct bundles of tangible and intangible assets that are effective in satisfying its customers and at the same time difficult for others to replicate. The company will be even more valuable if it can go on doing this over and over again by adding new assets to the bundle and replacing old ones in a cycle of investment and growth. In this case it will act as a machine for adding value to the replacement cost of its assets. Outside the firm an asset is simply worth its replacement cost, but inside the profit-generating environment of a successful firm it is worth more.

200

SECURITY ANALYSIS

Some firms, by contrast, may have a market value that remains below the replacement cost of their assets (q< 1) for extended periods. An example would be a firm that invests in a plant embodying an obsolete or otherwise unsuitable technology. Similarly, a company that constructs an expensive retail outlet on a low-traffic site may find it has created an internal asset with a market value below its replacement cost. More generally, companies can get in a chronic position of q < 1 if they continue to invest in poor projects whose rate of return is less than the cost of capital. In this case, they will find it very difficult to raise new capital. However in some cases, management may persist in reinvesting internally generated cash flow in low-return projects for nonfinancial reasons, driving q further down. Ultimately, a very low q may encourage a takeover in which the bundle of asset is split up and sold. Even if the assets cannot be liquidated for their full replacement value, the proceeds may be greater than the current market value of the firm as a whole.23 As shown in Section 6.2, we can think of q as a measure of profitability or rate of return. More precisely, q can be interpreted as the ratio of the rate of return on a firm's tangible assets to its cost of capital. Using the results of Section 6.2, we can write the theoretical share price (TP) in terms of RCAPS, the replacement cost of assets per share: TP = q*RCAPS.24 When q = 1, the company is, in effect, passively holding a bundle of assets. They may increase in value if the cost of replicating them rises, but they are unlikely to systematically increase much faster than the rate of inflation in the long run. When q > 1, the firm's assets are worth more than those assets would cost to replace. If the firm's strategy of asset utilization is easy to copy, new entrants will order more of these assets and use them in the same way, driving profitability and firm value down. Skilled companies, however, can find ways to bundle together their tangible assets with intangibles and accumulated skills in an operating environment, which can be very difficult to replicate. Shares in these firms will be more highly valued. If these firms can deter imitators or keep on finding new ways to utilize assets profitably, then this high value can be maintained for a long time. Some firms, on the other hand, find that their assets are worth less than they would cost to replace. This may be because they are caught with bundles of assets designed to serve markets that are declining or to support products that are obsolete. It may reflect a series of disappointing investment decisions or a glut in the supply of certain services. Such situations will be signalled by q < 1 because their value has fallen to reflect their expected low returns. We conclude that Tobin's q can, in principle, tell us a great deal about the intrinsic value of a company's shares. Its main attraction is that it puts replacement cost in the central position where it belongs. It is not a complete substitute for the detailed analysis of financial statements described in Section 7.3, but as a summary measure it appears to be superior to the price/earnings ratio. Further research is needed to see whether the promise of q theory can be realized in practice.

8

Options and Options Pricing

Many forms of option contracts are found in everyday life. These vary from the very informal to the standardized and precisely defined options traded on major options exchanges around the world. When you pay a nonrefundable deposit to reserve an outdoor tennis court for a particular day in the future, for example, you are entering into an informal options contract. You are paying a fee now in exchange for the right to buy a good or service in the future at a known price. If the day is clear, you enjoy a game of tennis. If it rains when the day arrives, or your prospective partner breaks his leg beforehand, you don't rent the court (the option is left unexercised). The most cash you can lose as a result of purchasing the option is the amount of the nonrefundable deposit, which is the price of the option. There are two broad classes of options: puts and calls. Our example illustrates some of the important characteristics of a call option. It involves the right to buy a good, service, or security in the future. The buyer of the option pays a fee for this right; that fee is the option price. In exchange for the option price, the seller of the option agrees to provide the good, service, or security at a fixed price, called the exercise price or striking price, if the holder of the option chooses to exercise the option. In this example, the striking price is the rental payable when the tennis court is actually used. Most options are valid for a fixed period of time, after which the right to exercise the option expires. The time period for which an option remains valid is known as the life of the option, and the last day on which it can be exercised is its maturity. The characteristics of a put option are virtually identical, except that the holder of the option has the right to sell a good, service, or security to the other party at an agreed exercise price until some future date, rather than to buy it. It 201

202

OPTIONS AND OPTIONS PRICING

should be noted that while the buyer of a put or call acquires a right (not an obligation), the seller of the option does incur a definite obligation. As a guarantee of his or her ability to meet this obligation, the seller may have to provide "earnest money," also called margin.1 In general, the original buyer of an option is not required to hold it until it matures. If the right embodied in the option is valuable to others, the option can be resold. Many options can be readily negotiated, which makes them financial instruments as defined in Chapter 1. Since the early 1970s, standardized options on stocks have been traded in organized markets; more recently, options on commodities, on bonds, and on futures contracts have been added to the list. Section 8.1 discusses the basic features of option contracts, with special reference to stock options, including the way in which the contractual elements of an option (such as the maturity or exercise price) have been standardized to facilitate trading. Section 8.2 examines various methods of valuing options contracts and how the value of a option will be influenced by its maturity, striking price, market interest rates, and the price of the underlying security. It also explores the ways in which call and put options may be combined to form various types of "spreads" and "straddles," while Section 8.3 analyzes the way in which options might be used to hedge a portfolio of stocks and hence their role as a risk management tool. We then explain how the shares in a levered firm can themselves be viewed as a type of option, and the implications of this for the pricing of stocks. Finally, options on objects other than stocks are discussed in Section 8.5.

8.1 THE BASICS OF STOCK OPTIONS

In this chapter we are mostly concerned with options on stocks; other options do not come up until Section 8.5. We first discuss the organization of trading in stock options and then proceed to a preliminary economic analysis by looking at the profits and losses resulting from buying or selling these options. 8.1.1 Institutional Aspects: Exchange-Traded Stock Options

Prior to the early 1970s, options on stocks were negotiated on an individual basis between two parties, commonly matched by a broker. Since this arrangement required the identification of a buyer and a seller with complementary needs at the same point of time, the transaction costs were high and the volume of trading was severely limited. The lack of standardization and the possibility of default by individual participants made it difficult to resell options after they had been written, so the options were illiquid. Today, puts and calls on shares are traded on most major stock exchanges

THE BASICS OF STOCK OPTIONS

203

in the United States and on the Chicago Board Options Exchange.2 Similar exchanges now exist abroad, particularly in London and Amsterdam. Options on objects other than shares are discussed in Section 8.5 and in Chapter 9. These exchange-traded options were made possible by standardization of the options contract in various dimensions. Instead of letting individual buyers and sellers agree on the precise terms of the contract, each exchange lists a limited number of expiration dates and striking prices. This standardization, typical of financial markets as defined in Chapter 1, served to reduce transaction costs and thus to make options readily negotiable. Thus an option for any particular month has its maturity on the third Friday of that month. Furthermore, each option is assigned to one of three maturity cycles. Options on some stocks at first had maturities on the January-April-July-October cycle, others on the February-May-August-November cycle, and the remainder on a March-June-September-December cycle. Because interest turned out to be concentrated on nearby maturities, however, the current month and the following month have been inserted into the list in each cycle.3 Only three maturities are listed (both for calls and for puts) at any one time; for instance, on April 24 a stock on the January cycle will have options listed for May, June, and July maturities; one on the February cycle will have May, June, and August listings; and one on the March cycle will have May, June, and September listings.4 Striking prices have been standardized by listing only multiples of $5.00 (except for low-priced stocks, where the multiple is $2.50). Initially, only striking prices close to the prevailing market price for the underlying security are listed; thus if at the first listing of the October option a stock trades at $57 per share, the initial striking prices will be $55 and $60. If the stock price subsequently moves significantly outside this initial range, new striking prices are listed as needed. For example, if the stock in question rises to $63, a striking price of $65 will be added to the list. The result is that toward the end of an option's life, a sizable number of striking prices may be open for trading.5 The number of shares per contract (100), along with rules pertaining to stock splits and dividends declared on the underlying security during the life of the option, have also been standardized by agreement among the options exchanges. In listed options, for example, the terms of the contract remain unaltered when a cash dividend is declared or paid. On the other hand, the options contract will generally be adjusted for splits and stock dividends. Another important innovation has been the interposition of an options clearinghouse (the Options Clearing Corporation in the United States) between buyers and sellers. Once an options price has been agreed in the market, the clearinghouse acts as the seller to all buyers, and as the buyer to all sellers. This arrangement has the important effect that the clearinghouse guarantees the performance of the contract, eliminating the need for either party to check the creditworthiness of the other prior to a trade. It also means that the buyer or seller of an option can close out his position at any time by purchasing an offsetting options

204


contract without having to locate the original counterpart to the transaction. Both aspects greatly facilitate the secondary market.6 Information on the prices of listed options is reported daily in the financial press. Table 8.1 reproduces listings for two stocks, showing first the name of the underlying security, with its closing price in parentheses. Then follow the volume of trading and the price (expressed on a per share basis) of each call and put currently offered.7 The explanation of these prices is the main topic of this chapter; as regards volume of trading, it will be noted that some options do not trade at all on any given day, and that volume tends to be larger when the striking price is close to the stock price. Some insight in the quantitative importance of trading in options on equities is provided by Table 8.2, which also shows how many options were exercised. From this table we can draw a number of conclusions: 1. The activity in exchange-traded options, as measured by the number of contracts traded, has declined in recent years (it reached a peak in 1987). It has fallen far behind the growth in stock market volume recorded in Table 5.1. 2. The Chicago Board Options Exchange dominates the industry with roughly two-thirds of the total volume and value. 3. Only about 5% of the options traded were exercised. The options that were not exercised must either have become worthless or liquidated by an offsetting transaction prior to expiration. Table 8.1 Sample Options Listings October Volume Ford Motor (40 1/4) 35 call 40 call 45 call 35 put 40 put 45 put Data General (10) 7 1/2 call 10 call 12 1/2 call 10 put 12 1/2 put

15

673

348 0 284 20 0 25 0 10 0

November Price

61/4 l 1/4

>/4

[a] 7/8

33/4

[a] 9/16

[a] 1/2

[a]

Volume

0 94 55

0

56 10

0 5 5 60 0

December

Price

Volume

[a]

60 90 97 33 95 0

2% 1/2 la] 1% 4 5/8

[a] 3/4 1/4 3/4

[a]

a

No trades (see text).

Source: Investor's Business Daily, September 23, 1992 (quotations for previous day).

276 624 102 0 271

Price

6% 2 9/16 3/4

7/16 2 1/8

[a]

2 13/16 1 1/16

5/16

[a] 2%


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Table 8.2 Trading in Stock Options (volume in millions of contracts, total value in billions of dollars) 1985

1990

1992

149 49

130 41

121 42

VOLUME OF TRADING

Chicago Board Options Exchange American Stock Exchanges Other exchangesa ALL EXCHANGES

34

39

233

210

39 202

38.4 11.6 9.1 59.1 254

55.4 12.8 10.8 79.0 380

44.5 14.1 13.6 72.2 357

10.5 4.5

12.1 5.8

11.6 5.7

VALUE OF CONTRACTS TRADED

Chicago Board Options Exchange American Stock Exchanges Other exchangesa ALL EXCHANGES Mean value in $ per option traded

OPTIONS EXERCISED (All exchanges) Number as % of number of options traded a

Includes the Pacific and New York Stock Exchanges.

Source: 1994 Statistical Abstract of the U.S., table 812.

8.1.2 The Payoff from Buying and Selling Options

We now make a start with the economic analysis of puts and calls on stocks. Figure 8.1, known as a payoff profile, shows the profit or loss made by an investor who purchases a call option on a stock as a function of the stock price.8 Whenever the market price of the stock (Ps) remains below the striking price stated in the option contract (Px), the investor will not exercise the option since the stock can be procured more cheaply direct from the open market. The option is then said to be "out of the money." If an option remains out of the money until maturity, nobody will want to exercise it and it expires, worthless. The buyer will then suffer a loss equal to the price he paid for the call (P c ), plus the interest foregone on the initial outlay. If the price of the underlying stock rises above the striking price (i.e., the option comes "into the money"), the investor will have a net payoff Z equal to the market price of the stock, less the exercise price (at which he has the option to buy the stock), less the cost of buying and holding the call option.9 In formula Z = Ps — Px — P c (1+rT), where r is the short-term rate of interest and T the time interval between the acquisition of the option and its exercise, also known as the holding period. This net payoff need not be positive, since the profit from exercising the option (Ps — Px) may not be enough to offset the original cost of the option plus

206


Figure 8.1

Payoff profile for the buyer of a call

interest foregone. Even if there is an overall net loss, however, it will be advantageous to exercise the option whenever Ps exceeds Px. In practice, there may be transaction costs associated with the exercise of an option, so that Ps has to exceed Px by more than those costs. The relationships are reversed where the investor buys a put option. As illustrated in Figure 8.2, the option will remain unexercised if the market price of the underlying stock remains above the exercise price. This is so because it is then more profitable to sell the stock in the market than to "put" (sell) it through the option. In this case, the investor would have a loss equal to the price paid for the unexercised put (Pp) plus interest foregone. If the price of the stock were

Figure 8.2

Payoff profile for the buyer of a put


Figure 8.3

207

Payoff profile for the writer of a call

to fall below the exercise price, however, the net payoff Z would be given by Z = Px — Ps — P p (1+rT). Whether Z is positive would again depend on the cost of the option and on the interest foregone, and also on any transaction costs, as in the case of a call. The net payoff for the seller (usually called the writer) of a call option is shown in Figure 8.3. Obviously, it is the mirror image of the payoff for the holder. The reader will have no difficulty in drawing a similar picture for the writer of a put option. 8.1.3 Combinations of Options

In our discussion of options so far we have looked at the pattern of profit and loss associated with the buying or selling of one put or one call considered in isolation. The buyer of a call, for example, benefits when the price of the underlying stock rises enough to move the option into the money. Similarly, the buyer of a put benefits when the stock price falls significantly. By combining options it is possible to create a different set of payoff profiles. In this section we examine the more common of these combined positions and their payoff profiles if held to maturity. The simplest option combination is the straddle, in which the investor buys both a put and a call on the same stock and where both options have the same maturity and striking price. If the price of the stock remains steady throughout the life of the straddle, the investor will lose the cost of the position—that is, the price paid for the put plus the price paid for the call. Breakeven will occur when the stock price rises or falls by an amount equal to the cost of the straddle. Any larger rise or fall in the stock price at maturity then nets a dollar for dollar gain to the straddle holder. This payoff profile is charted in Figure 8.4, where the common striking price is $15, the price of the call is $2, and the price of the

208


Figure 8.4

Payoff profile for the buyer of a straddle

put is $2. The figure shows both the straddle and its components; the payoff on the straddle, needless to say, is the algebraic sum of the payoffs on the components. This identity will help in drawing the payoff profiles for other combinations of options. The reverse position of the writer of a straddle (selling the equivalent put and call simultaneously) is left for the reader to explore graphically or otherwise. In this case, the writer profits when the underlying stock price exhibits little change over the life of the straddle and loses when it moves substantially either above or below the common exercise price. A straddle, therefore, may be interpreted as a bet on the volatility of the stock price: the buyer of a straddle bets on small volatility and the writer on large volatility. A second major set of composite positions involve the purchase or sale of a put and a call, again on the same stock and with identical maturity, but with different exercise prices (that of the put usually being less than that of the call). Such a combination is an example of an option spread; in this case, it may be called a put-call spread. Compared with a straddle, this spread requires a larger movement in the stock price before its holder will profit, and conversely the writer can withstand a larger price movement before being forced into loss. The payoff profile for the purchaser of a spread position is again left as an exercise. Another example of an options spread is obtained by purchasing a call at one striking price and selling a call on the same stock with the same maturity but a different striking price. Such a position is known as a price or vertical spread.10 An investor who is mildly bullish on the price of a stock might "buy the vertical spread"; in other words, he or she might buy the option with the lower exercise price and sell the call with the higher exercise price. The total investment (maximum loss) here would be smaller than that required to buy a call alone since some of the cost of the option with the lower exercise price


209

(which will be the more expensive) is offset by the proceeds of selling the other call.11 If the stock does not reach either striking price, the investor loses the difference between the original prices of the two calls. The maximum profit on the spread is also determined in advance. If the stock price rises dramatically, both options will be exercised. In that case, he or she buys at the low exercise price and sells at the higher one. The total profit will then be equal to the exercise price of the call sold less the exercise price of the call bought less the cost of call bought plus the proceeds received from the call sold. Yet another form of spread involves simultaneously buying and selling two call options on the same stock with the same exercise price, but with different maturities. This is called a time or horizontal spread. The buyer of a horizontal spread who is bullish on the price of a stock will purchase the call with the long maturity and sell the corresponding call with a shorter maturity. Again, the maximum loss occurs when both options remain out of the money and is equal to the difference between the price paid for the distant option and the price received for the call with shorter maturity. The maximum profit from the spread itself (assuming the longer option is sold when the nearer one matures) would occur if the stock price were exactly at the exercise price on the maturity date of the near option. In this case, the near option would be worthless to its holder but the distant option, which still has some months to run, would have a value. The profit from the horizontal spread would then be equal to the current value of the distant call plus the proceeds from sale of the near call, less the original cost of the distant call. Numerous other possibilities are available, including selling rather than buying horizontal or vertical spreads, and butterfly spreads that involve buying two calls and selling two others on the same stock: one with a higher exercise price and one with a lower striking price than that of the calls originally purchased. These butterfly spreads will appeal to traders who believe that the price of the option in the middle is "out of line" with the prices of the other two. The reader is encouraged to draw the payoff profiles for such spreads. 8.1.4 Combining Options with Stocks

So far we have discussed combined positions including options only. Another important class involves combinations of a stock and options on the same stock. A fairly common option-stock combination arises when a certain number of shares is bought and an equal number of calls is written against them.12 This transaction is known as writing a covered call; an option written without an offsetting position in the underlying stock is said to be naked. The payoff profile is shown in Figure 8.5, where the stock component is simply a straight line with a slope of 1 going through the price of the stock when the call was written. It can easily be verified that the profile for a covered call looks identical with the one for writing a naked put.13 As does the writer of a naked put, the writer of a

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Figure 8.5

Payoff profile for the writer of a covered call

covered call runs the risk of a substantial loss if the price of the underlying stock falls by more than the call premium he or she has collected. Actually there are differences between the two transactions that are not apparent from the profiles, which lack a time dimension. Unlike a call, a stock has an infinite maturity and may earn dividends; the transaction costs, which have mostly been ignored so far, may also be different. Another common example is buying both a stock and a put on the same stock for the same number of shares. The resulting payoff profile looks the same as that from buying a call (Figure 8.1), but again there are differences that do not show up in the profile. More generally, it should be noted that payoff profiles, while useful in explaining the basics of options, have severe limitations because they only show the initial position. In Figure 8.5, for instance, the broken line for the call is not really correct: If the market price were to fall below its initial value, the call would be worth less, as explained in Section 8.2. The covered writer could then buy back the call for less than she had originally sold it for, thus offsetting some of her loss on the stock. Payoff profiles also fail to reflect the declining value of options as they approach maturity. Needless to say, many other combinations of stocks and options are possible, but we cannot consider them all. Only one of these deserves separate discussion because it leads to a general proposition, derived in Section 8.1.5, concerning the relation between put and call prices. It merges the two cases just discussed. Suppose an investor buys a stock and a put, and also sells a call; the two options, which have identical exercise prices and maturities, are for the same number of shares (say one), as the stock itself. When the payoff profile for this "balanced stock-put-call position" is drawn, it turns out to be simply a horizontal line parallel to the price axis. A numerical example may be helpful for clarification. Let the exercise price


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of the two options be $50 and let the initial purchase price of the stock be $47. If the stock price is below $50 when the options mature, the investor will exercise his put at $50, thus making a profit of $3 on the stock, from which the net cost of the two options must be deducted. If the stock price is precisely $50 at maturity, neither option would be exercised and the stock could again be sold for a profit of $3. For a stock price at maturity above $50 (say $52), the investor will find that the call he has sold will be exercised by its buyer, leading to a loss of $2 on the call that should be offset against a profit of $52 - $47 = $5 on the stock. Hence in all cases the payoff is $3 (the difference between the initial market price of the stock and the exercise price of the options), less the net cost of the options.14 8.1.5 The Put-Call Parity Theorem

The preceding example gives rise to an important theorem first stated by Stoll (1969), though it must have been known to practitioners before then. Since the net profit or loss is independent of the ultimate market price of the stock, the position we constructed is riskless. We know from Chapter 6 that the expected profit on a riskless position must equal the return on the capital invested at the default-free interest rate. In this case the capital invested is Ps + Pp — Pc, where Ps is the initial market price of the stock, Pp the price of the put, and Pc the price of the call. The payoff is Px — Ps + Pc — Pp, where Px, as before, is the exercise price of the two options. Consequently we must have Px — Ps + Pc — Pp = rT(Ps + PP- Pc), which can be simplified to Pc - Pp = Ps - (1 + rT) - 1 P X , where r is again the short-term interest rate and T the holding period (which in this case is the time interval between the present [t] and the expiration date of the option). The conclusion is known as the Put-Call Parity Theorem The difference between the prices of a put and a call on a nondividend paying stock, both options having the same maturity (prior to which exercise is not possible) and exercise price, must equal the current price of the stock less the present value of the exercise price. In the preceding example, suppose the interest rate is 12% per year and the holding period three months; then rT=0.03 and the present value of the striking price is $50 1.03 = $48.54. Therefore the put price must exceed the call price by $1.54 ( = 48.54-47.00). This stands to reason since the put is "in the money" and the call "out of the money." By contrast, if the striking price had been $45, the call price would have been $3.31 ( = 47-45 1.03) higher than the put price. It also follows that if the put and the call for a certain maturity are both "at the money" (that is, at the current price of the stock), then their values are approximately equal.15 A case in point can be found in Table 8.1 for Data Gen-

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eral, which closed at $10 and does not pay a dividend. We see that the last price of the October 10 call was minimally different from the last (not necessarily simultaneous) price of the October 10 put, but that for the November maturity the two prices were the same. This conclusion is useful in understanding the relation not only between puts and calls (Section 8.2.6) but also between options and futures (Section 9.1.2). Put-call parity (PCP) is important in the theory of options because it involves very few assumptions; the critical assumption (namely, that transaction costs are zero) will be discussed at the end of this section. The simplest application of PCP follows immediately from the theorem as just stated, where the difference between the call price and the put price is given as a simple function of four parameters (the stock price, the exercise price, the interest rate, and the remaining life of the option.) Thus the put price can be found if the call price— together with the four parameters—is known; the determination of the call price is the subject of the next section. An example will be presented in a moment. First we deal with another application of PCP, made possible by solving for rT in the last displayed equation, which leads to

As an illustration, consider the Data General options of Table 8.1, specifically the 12 1/2 options expiring in December (that is, on December 18, the third Friday in that month). The formula then tells us that rT = 0.01538. Since the quotations are for September 22, the options had a remaining life of 87 calendar days, equivalent to 0.2384 years, which implies r = 6.45%. This "implied interest rate," incidentally, does not allow for possible compounding; to get compound rates, we should replace (1 + rT) in the preceding formulas with e-rT. The numerical difference between these two expressions is quite small unless rT is large; in the present illustration, for instance, use of compound-interest formulas would lead to r = 6.34%. For simplicity's sake, compounding will be ignored until further notice. The implied interest rate that has just been calculated applies in principle to all puts and calls that are (or could be) traded on any given day. It can therefore be used to estimate the value of a December 10 put, for which there is no price in Table 8.1. The call with the same striking price traded at $1.0625, and it follows from the theorem that Pc-Pp= 10- 10/1.01538 = 0.51. Consequently, the theoretical value of the December put is 1.0625-0.51 = $0.55, or about 9/16 in the quotation system used for stock options. To conclude the discussion of PCP, we have to say something about its empirical validity. The main weakness of the theorem is that it neglects transaction costs, yet the riskless put-call-stock combination from which the theorem is derived involves three different transactions (two in options and one in the

THE VALUATION OF STOCK OPTIONS

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stock), each of which may involve a bid-ask spread and—if the arbitrage is undertaken by an outside investor—a commission. In reality, therefore, PCP is more likely to be satisfied in some average sense than exactly in all cases.

8.2 THE VALUATION OF STOCK OPTIONS

The valuation of options contracts is among the most interesting—and also the most demanding—topics to be dealt with in this book. Long before stock options had reached their present importance, scholars and financiers had wondered how their prices were determined.16 It was commonly believed that option prices somehow depend on traders' subjective expectations and risk preferences while stock prices reflected market equilibrium. This view is not helpful since these determinants on the individual level cannot be observed directly. A breakthrough in options theory came when it was realized that stock prices and options prices depend on the same set of expectations, and that this joint dependence permits the development of explicit formulas for option prices (discussed in Section 8.2.3). Basic to an understanding of the theory is a distinction applicable to both puts and calls: The contract may state that the holder can exercise the option (1) only on maturity, in which case it is known as a European Option, or (2) at any time up to maturity, in which case it is known as an American Option.17 The European type happens to be easier to analyze, so we shall consider it first. Remaining on an intuitive level, we may begin by analyzing what factors might logically play an important role in determining the worth of a European option to its holder. The first such factor is clearly the price behavior of the underlying stock. Figure 8.1 shows that the higher the stock price goes, the more valuable the call option becomes to its holder.18 A large increase in the stock price will be more likely to occur if the stock is volatile relative to the rest of the market. The first important conclusion with regard to options, therefore, is that the call option is more valuable the more volatile the underlying stock. This is in direct contrast to the valuation of the stock itself, where (as we saw in Chapter 6) volatility tends to reduce the stock's value to risk-averse investors. The most that the holders of a call option will lose if the price of the stock declines is the price they originally paid for the call, which will then remain unexercised. The opposite is true when a stock pays a cash dividend. The shareholders face a decline in the stock price after the dividend is declared, but this decline is offset by the dividend receipt, to varying degrees depending on their tax position, the transactions costs they face, and their income preferences. The holder of a call option, however, will almost certainly lose as the chance that the stock price will exceed its striking price declines in the wake of an outflow of dividend cash from the firm.19 The opposite holds for a European put.

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The second set of important factors in option valuation are the characteristics of the option contract itself. The higher its exercise price, the lower the value of a call and the higher the value of a put (for any given current price of the stock). A higher exercise price for a call, for instance, means a greater likelihood that the call will be out of the money at maturity and hence that it will not be exercised. Although they refer to American options, the option prices shown in Table 8.1 illustrate this point, and also the next one. The second relevant characteristic of the option contract is its maturity, which determines its remaining life T. The longer its remaining life, the greater the chance that the stock price will rise above the exercise price.20 Moreover, since the exercise price of a European call is the amount that must be paid on maturity, a call with a long maturity will have a lower effective exercise price when discounted back to the present. In other words, since a dollar in the future is worth less than a dollar paid now, the same exercise price is actually lower the further into the future it must be paid. The corresponding analysis for a put is left to the reader. It follows that the final factor of importance in valuing an option is the prevailing market interest rate. In fact, it turns out to have a much more pervasive influence than simply as a determinant of the present value of the exercise price, as will become apparent. Before discussing that issue, however, let us pursue our logical intuition a little further on the case of nondividend paying European calls. The next step toward a valuation model for these calls is to understand some simple bounds outside of which the price cannot move. The first of these stems from the fact that an option to buy one unit of a stock can never be worth more than the market price for which that stock can be resold. Algebraically Pc(t), the price of the call at time t, must be less than or equal to the price P s (t) of the underlying stock at that time: P c ( t ) < P s ( t ) . If this were not the case, it would be cheaper to buy the stock directly in the market than by exercising the call, even at a zero striking price. Secondly, it should be clear that an option to buy a worthless stock will itself be worthless, so that Pc = 0 if PS = 0. The value of an option, however, can never be negative since its holder always has the right to leave it unexercised rather than exercise it at a loss.21 The option holder, therefore, cannot lose more than the cost of the option. A further boundary may be defined by considering the exercise of a European call at maturity, that is at time Tl. Since the option was established at time t and was assumed to have a remaining life of T, we have Tl=t+T. On that day the price of the call must be at least equal to the difference between the price P s (T 1 ) of the stock and the exercise price (Px). Consequently P S ( T 1 ) - P X is the profit to be made by exercising the option to buy the stock at Px and immediately selling it in the market at Ps(T1). If this potential profit were greater than the cost of the call, arbitrageurs would be buying up calls, exercising them, and


Figure 8.6

215

Upper and lower bounds for a European call option with no dividends

selling the stock to make a windfall gain. The resulting demand for calls would force their price Pc to rise until: P C (T 1 )>P S (T 1 )-P x ,and hence the potential for windfall gain would be eliminated. Taken together, these constraints define upper and lower bounds for Pc relative to Ps forming a parallelogram of the form shown in Figure 8.6. 8.2.1 The Expected Payoff of a European Call

As just noted, the proceeds from exercising a European call at maturity T1 equal PsT-Px , where Ps(T1) has been abbreviated to PsT. Disregarding transaction costs, exercise will be profitable only if P sT >P x . The expected payoff EP may therefore be written as a conditional expectation: EP = E(P s T -Px\P s T >P x ), where the second expression indicates the condition under which the expectation is to be evaluated. The expectation of a difference is equal to the difference of the separate expectations, so we can also write EP = E(PsT\PsT>Px)-E(Px\ P ST >P x )The first term on the right will be called E0. In the second term on the right Px is not a random variable but a known constant; it can therefore be put before the expectation operator and the term becomes Pxprob(PsT>Px), or PXE1 for short. Thus we get EP = E 0 -P x E 1 . The buyer of a European call, purchased at time t, has an initial investment of Pct = Pc(t). The expected payoff occurs after the option has completed its remaining life

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T; to calculate the return on this investment, we must discount the expected payoff at an (as yet unknown) rate of rc per annum.22 The expected return on the investment is then

The problem of valuing a European call has thus been reduced to determining the discount rate rc that will bring the expected return on the call in line with alternative investments, such as buying the stock itself and holding it for the same length of time T. For this purpose we turn to the Capital Asset Pricing Model (CAPM). 8.2.2 Application of the Capital Assets Pricing Model to Options

In this section we continue to lay the groundwork for an explicit formula giving the expected value of a European call.* This formula, discussed more fully in the following section, was first derived by Black and Scholes (1973), who thereby brought a long search to a successful conclusion. Its discovery was not only an academic achievement; it has also had a major impact on the actual practice of option trading.23 The widespread acceptance of the Black-Scholes formula is the more remarkable because it is based on a number of simplifying assumptions whose realism is open to question. These assumptions, quoted with minor changes from the original source, are 1. The stock price follows a random walk in continuous time with a coefficient of variation24 proportional to the stock price. 2. The coefficient of variation of the return on the stock is constant over time. This implies that the distribution of stock returns is lognormal. 3. The short-term interest rate is known and constant through time. 4. The stock pays no dividends or other distributions. 5. There are no transaction costs. These assumptions include those underlying the CAPM, which can therefore be legitimately applied. The expected value w of a European call under these assumptions depends only on the stock price Ps and time t, and on three known parameters, namely, the interest rate r, the holding period T, and the standard deviation of the return on the stock. Thus we can write E(P c ) = w(Ps,t;r,T, ), where the parameters are separated from the principal variables by a semicolon; in fact, these parameters will usually be suppressed. To use CAPM, we must first look at expected returns. Since by assumption the stock on which the call is written does not pay any dividend its expected return (relative to the initial investment of Ps per share) in any short time interval * Readers whose knowledge of calculus stops short of partial derivatives may skip this section.


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t is simply the expected price change E( P s /P S ) over that interval. According to CAPM, this expected return satisfies the equation

where r is the return on a default-free asset, a the additional return on the market portfolio, and s the stock's beta. A similar equation must hold for the option, which is also a financial instrument:

where C is the beta of the call option. The two betas occurring in Equations (8.1) and (8.2) are obviously related to each other. To see how they are related, we consider the dependence of the call option value w on the current stock price Ps as given by the partial derivative w(P s ,t)/ Ps = w1, where the subscript reflects the position of Ps as the first argument of w(P s ,t). Thus a $1 difference in the stock price, everything else (including time) remaining the same, leads to a $w1 difference in the expected value of the option price.25 When this relation is applied to the changes in Ps and Pc considered in the preceding paragraph, we find that E( Pc) = w1 Ps, from which it follows that

The first factor on the right-hand side is known as the option elasticity. A further consequence is that

which is the desired relation between the two betas. Although we cannot prove it here, it is intuitively clear that the beta of a call will normally exceed the beta of the underlying stock. The derivation of an explicit formula for the expected option value is equivalent to finding the function w(Ps,t) that satisfies Equations (8.1) through (8.3). The mathematics needed for this purpose is well beyond the level assumed in this book, and we will not try to paraphrase it.26 8.2.3 The Black-Scholes Formula for a European Call

In its original form, the Black-Scholes formula expresses the expected value of a European call in terms of two variables (the stock price and the current date) and four parameters (the exercise price, the risk-free interest rate, the remaining life of the option, and the volatility of the underlying stock). In our notation the formula reads:

where (repeating some of the previous definitions for convenience)

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Pc = the price of a European call Ps = the price of the underlying stock Px = the exercise price of the option r = the continuously compounded annual risk-free rate of interest Tl = the date on which the option expires t — the present date N(z) = the probability that a random variable will exceed z given a normal distribution with a mean of zero and a variance of 1,

=the standard deviation of the stock price, considered as a random variable Since the original Black-Scholes formula is somewhat complicated, we shall now present it in a simplified appearance. The simplification is accomplished by combining the variables and parameters into only two arguments; since the process requires no additional assumptions, it does not restrict the validity of the formula in any way. The simplified Black-Scholes formula may be written

where the new variables are QC = P C /P S ,which is the ratio of the price of the call to the price of the stock, and y = (P x e - r T )IP s , the ratio of the present value of the exercise price to the stock price. This substitution also gives a simpler form for two components of the Black-Scholes formula:

The last two formulas involve two more new variables: T=Tl — t, the remaining life of the option expressed in years, and T= T1/2;this is the customary standard deviation of the return on the stock multiplied by the square root of the remaining life. It corresponds to the standard deviation of the stock price during the remaining life of the option and will be called the fractional standard deviation.27 Evidently if the remaining life is one year (T= 1), the customary and fractional standard deviation are the same, from which we see that the customary standard deviation is actually on an annual basis.


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The interpretation of the simplified formula is easiest in the special case where the stock price is the same as the present value of the striking price. This is almost the same as saying that the call option is "at the money," but not quite because the striking price is discounted; when the interest rate is low or the remaining life is short, discounting will have little effect. It implies y=1, log y = 0, and consequently

In this particular case, the ratio of the call price to the stock price is equal to the difference between two values of the cumulative normal distribution (with zero mean and unit variance), one calculated at a point located one-half of the fractional standard deviation above the mean and the other at a point the same distance below the mean. Since the normal distribution is symmetric around the mean, the area under the normal density curve between each of these two points and the mean is the same. We now return to the general case. As an illustration of the Black-Scholes formula, which can be easily programmed for a calculator or computer, the call option values corresponding to selected parameters (as defined above) are given in Table 8.3. The option values are given as a percentage of the stock price,

Table 8.3 Theoretical Value of a European Call as a Percentage of the Stock Price =0.2

T

x=

0.75

1.0

=0.3 1.25

0.75

1.0

1.25

25.38 25.80 26.30 26.84 27.41 27.99 28.58 29.16

4.03 5.83 7.27 8.51 9.64 10.67 11.63 12.54

0.04 0.36 0.89 1.52 2.20 2.90 3.60 4.31

25.75 26.53 27.36 28.22 29.08 29.94 30.79 31.63

4.28 6.34 8.04 9.53 10.91 12.19 13.40 14.56

0.05 0.42 1.07 1.84 2.69 3.58 4.48 5.38

r=.05

.1 .2

.3

.4 .5 .6 .7 .8

25.37 25.75 26.12 26.51 26.91 27.31 27.73 28.14

2.77 4.07 5.12 6.05 6.89 7.67 8.42 9.12

0.01 0.03 0.13 0.32 0.57 0.87 1.20 1.56

25.75 26.49 27.22 27.96 28.69 29.42 30.15 30.87

3.04 4.61 5.94 7.15 8.28 9.35 10.38 11.37

0.00 0.04 0.19 0.46 0.82 1.26 1.76 2.30

r=.10 .1 .2 .3 .4 .5

.6 .7 .8

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which is equivalent to putting the stock price at $100 throughout and expressing the option value in dollars. From this table it can be verified that the results of the Black-Scholes formula are consistent with the basic logical results presented earlier, namely, that the price of a European call option will be higher (all else equal) • • • • •

The The The The The

higher the initial stock price lower the exercise price more volatile the price of the stock longer the remaining life of the option higher is the risk-free interest rate

Intuitively, the last result reflects the fact that if the risk-free rate rises, so must the required return on a perfect hedge. The achievement of this higher return implies that the investor receives a higher price for each call option sold. 8.2.4 Alternative Derivations of the Black-Scholes Formula

Although the final Black-Scholes formula is relatively simple, its derivation (given only in part) is not. More elementary proofs have been attempted, and we now present one such effort due to Cox and Rubinstein (1985). With the earlier discussion of option-stock combinations in mind, we may think about this problem in terms of a portfolio consisting of a long position in the stock and a short position in the related call option; in other words, buying a stock while also selling one or more calls against that stock. Suppose you paid $10 for one share and sold one European call with a striking price of $10 and a maturity of one year for $1. If at the end of the year the stock is trading in the market at a price higher than $10, the holder of the call will exercise the option requiring you to sell the stock for $10, so you wind up with gross revenue of $11. If instead at the end of the year the stock was still trading at $10, the holder would not benefit by exercising the call; you can then sell the stock on the open market for $10 while keeping the proceeds of selling the call, again leaving you with $11. In this example of a covered call the holder of the stock is hedged against a rise in the stock price, as we know already from Section 8.1.3. If the price of the stock began to fall, however, the holder would stand to lose. She could protect herself by immediately selling more calls against her shares in order to maintain the ultimate gross revenue at $11. In deciding how many calls to sell, she would have to take into account that at the lower stock price, each call sells for less. In a world without transactions costs, it is possible to continually readjust the ratio of calls to the price of the stock so as to protect the value of the portfolio against any changes in the stock price, thus eliminating risk altogether.


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What return should an investor earn on this risk-free portfolio? The answer is the risk-free interest rate. The reversal of this chain of reasoning allows us to derive the relationship between the price of a stock and the price of a call option on that stock. Specifically, using the requirement that a perfectly hedged portfolio must earn the riskfree rate, we can work back through the definition of the perfect hedge as a mix of a long position in the stock and a short position in the call option to derive a formula for the price of the call itself. This procedure is best illustrated by example. Suppose there are two possible future states of the world, a boom and a recession, each with a 50% chance of occurring. If the economy goes into boom, the price of our stock will increase by f% to a new price (1 +f)Ps. In forming a hedged portfolio, however, we sold a number h of call options for every unit of stock we hold. Any increase in the price of the stock above the exercise price of the call option will therefore be transferred to the holder of the call at an exercise price of Px. The total value of our hedged portfolio in a boom will therefore be (1 +f)Ps-h{ (1 +f)Ps — Px}: In other words, the new value of the stock, less that part of the benefit accruing to the holder of the call option multiplied by the number of calls we sold (h). If, on the other hand, the economy goes into recession, the value of our stock will decline by g%, while the calls will not be exercised, so that our portfolio will be worth simply: (1 — g)Ps. Now if the portfolio is perfectly hedged its value must be equal whether or not the stock price rises or falls, so that (1 +f) Ps — h{ (1 +f)Ps-Px} = (l -g)Ps, that is, the value in boom must be the same as the value in recession. We can use this equation to solve for the number of calls h that must be sold to achieve a perfect hedge:28

Now recall that the amount we have invested in the hedged portfolio is equal to the amount we originally paid for the stock (Ps) less the cash we received from selling the call options (hPc), where Pc is the price received for each call. This investment should return the risk free rate so that at the end of the period it is worth (1 +r)(P s — hPc). Equating this to the assumed value of the portfolio in a boom, we have (1 + r)(Ps-hPc) = (1 +f)Ps-h{ (1 +f)Ps-Px}. Substituting for the hedge ratio h, and solving this equation for the original price of the call Pc we have:

What we have then is a formula for the price of a call option in terms of the price behavior of the underlying stock, the exercise price of the call, and the

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risk-free rate of interest. This case is the simplest of what in the finance literature is called the binomial option pricing formula. Given the relevant data, it can be used to directly compute the equilibrium price of a call option. For example, suppose the present price of a stock is $50 and it is estimated to be equally likely to fall to $30 (g = 40%) over the coming year as it is to rise to $80 (f=60%). If the interest rate is 10% per year, the price of a 12-month call option on that stock with an exercise price of $60 would be:

It should be clear, however, that this relationship has major limitations as a satisfactory model of option pricing. Specifically, the range of stock price behavior that it can handle is very narrow, since in reality that behavior can rarely be expressed in terms of only two states of the world. A number of models incorporating richer specifications of stock price behavior have therefore been developed. Their basic logic parallels the intuitively appealing derivation we have just given. But the Black-Scholes pricing theory, thanks to its effective use of advanced mathematics, is less restrictive than any binomial-type model and continues to be most widely used. 8.2.5 Other Option Models

While a very significant improvement, the Black-Scholes model still places important restrictions on the range of stock price behavior that it can validly handle. Empirical investigations (such as Black, 1976) have concluded, for example, that the variance of returns tends to increase as the stock price declines. This condition may reflect the fact that in a levered firm with fixed interest commitments, shareholders are left with a rather erratic residual when average earnings are low. In answer to this problem, Cox and Rubinstein (1975) proposed the constant elasticity of variance model in which the variance of returns depends on the level of the stock price. While the basic construction is similar, this requires replacement of the Black-Scholes normal distribution with an alternative statistical distribution, the gamma density function. Finally, Merton (1976) has formulated a model in which, in addition to "normal" random fluctuations around a trend, stock prices are allowed to take discrete "jumps" that might result from events such as release of unexpected information about the firm's performance, sudden obsolescence as a result of technological breakthrough, or decisions in major lawsuits affecting the firm. This so-called jump-diffusion model derives an adjustment to the basic Black-Scholes option price to account for the probability and size of jumps in the price of the underlying stock. Empirical evidence concerning the model's explanatory performance (e.g., Beckers, 1981) has been favorable, although the


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impact of jumps appears to be relatively small, particularly in a diversified options portfolio. The additional computational complexity, meanwhile, is considerable, leading most practitioners to employ the simpler binomial or BlackScholes specifications. 8.2.6 Some Extensions of the European Call Formula

Before leaving the topic of option pricing, a number of extensions of the basic formulae to encompass dividend payments, American (flexible maturity) calls, and put options merit brief discussion. The first approach to dividends involves an assumption that regular dividend payments are known in advance over the life of the option. In many cases such an assumption seems acceptable since the life of most options is relatively short (usually less than 9 months) and most stocks pay regular dividends that are changed relatively infrequently. In this case it is possible to allow for dividends simply by subtracting the present value of the known dividends from the stock price in our valuation equations; that is, if one dividend of $D was due during the life of the option six months from now, the stock price Ps would be replaced with P s , - D e . - r / 2 . A similar approach is adopted when the dividends are assumed to be of uncertain size; however, in this case the certainty equivalent of the distribution of possible future dividends must be subtracted from P5. The real problem is then to specify this distribution. Some researchers have suggested the assumption of a constant dividend yield so that the actual dollar value of dividends received varies in line with movements in the stock price. This means that Ps is replaced by P s e - d where d is the constant dividend yield over the life of the option. We now turn to the complication introduced by the right to exercise prior to maturity embodied in an American option. At the end of Section 8.2 we showed that at maturity the option cannot be worth less than the difference between the price of the stock and the exercise price; otherwise, a riskless arbitrage profit could be made simply by buying the option, exercising it, and immediately selling the stock on the market. The counterpart of this lower boundary prior to maturity of the option will be the price of the stock at maturity less the present value of the exercise price (the amount of funds that must be invested in risk-free bonds now so that the proceeds will be sufficient to cover the exercise of the option at maturity). Figure 8.7 plots these secondary boundaries for different possible stock prices and different dates (tl,t2, • • •) prior to maturity. For very high prices of the stock, the value of the option will approach the bound; in other words, it will be worth little more than the value to be derived from exercising it. This limit exists because the chance that the stock price will go even higher is very small so the additional "speculative" value that the call had at low stock prices will now be minimal. An important point to notice from Figure 8.7 is that at any time an option

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Figure 8.7

The maturity-value relationship for an American call option

will always be worth more (or, at worst, as much) left alive (unexercised) than exercised. This fact means that, in the absence of dividends, it will never be optimal to exercise an American option prior to maturity. The reason is that by exercising an option you forego the chance to reap the benefit of an increase in the price of the underlying stock, and it is this chance, after all, that gave the call its value in the first place.29 It follows that the Black-Scholes formula also applies to American calls on shares without dividends. The reason it might prove rational to exercise an American call before maturity is the right to dividends. Suppose that after some date (t = 1) a stock will trade in the market "ex-dividend" (i.e., a buyer after that date will not have the right to the forthcoming dividend when paid, which will instead go to the previous holder of the stock). In this situation it may be optimal for the holder of an American call option to exercise it immediately before the stock stock goes exdividend. Thus the holder can capture the dividend payment that he or she would lose if the option were exercised at a later date. More precisely, it will be optimal to exercise the call if the value of the option unexercised is less than the value of exercising it at t = 1. The value if the option is exercised will be equal to the ex-dividend price of the stock, plus the amount of the cash dividend, less the exercise price:30 Pc0 is a measure of risk aversion. There are no financial or other constraints; in particular, it is not assumed that the trader's overall position is zero (which would make the trader a hedger in the sense of Chapter 8). The first-order conditions for a maximum are

Because these equations are linear in the unknowns, they can be solved as follows:

These formulas can be simplified by introducing realistic approximations. Since 0 and 1 are normally close to each other, we can assume them to be equal with a common value . Equations (10.9) and (10.10) then reduce to

Now we know that usually the cash-futures correlation is close to 1, the main exception being the harvest period in agricultural commodities.22 If so, it follows from Equations (10.11) and (10.12), which have the same denominator, that x0 is close to being the negative of x1, and consequently our trader is almost a hedger as defined in Chapter 9. In fact, his or her total net position is

which for plausible values of the parameters is a small number. Whether the trader is a long hedger or a short hedger depends on 0 and 1, which reflect

HEDGERS, SPECULATORS, AND MARKET EQUILIBRIUM

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his or her expectations concerning the change in the spot price and the futures price, respectively. Thus, if 0> 1, it can easily be verified that the trader will be long in the cash market and short in the futures market—that is, he or she will be a short hedger.23 10.3.2 Hedging Effectiveness

Since no futures market with adequate liquidity can provide a perfect hedge, the suitability of a futures market for hedging a trader's exposure to the cash market is a matter of degree. Among the measures of hedging effectiveness that have been proposed we shall present those due to Ederington (1979). The simplest of the two Ederington measures refers to the case of "full hedging," where the futures position is the exact opposite of the cash position. The risk faced by a fully hedged trader is that the "basis" will move against him.24 The "basis," in this case, is the difference between a particular cash price (not necessarily the one underlying the futures contract) and the price of a particular futures contract (not necessarily the expiring or dominant one). Risk is measured by the variance of the price in question. Then full hedging effectiveness (FHE) can be defined as 1 minus a ratio whose numerator is the variance of changes in the "basis" and whose denominator is the variance of changes in the cash price. If the "basis" remains constant over the time interval relevant to the hedger, its variance is 0 and the full hedging effectiveness is 1, indicating a perfect hedge. If the two variances are equal, the full hedging effectiveness is 0, so hedging is pointless. The second Ederington measure recognizes that, as shown in Section 10.3.1, it may not be optimal to be fully hedged. If the correlation between a particular cash price and a particular futures price is less than perfect, a better combination of risk and return is obtained by "partial hedging," where the futures position is less than the cash position. The optimal ratio of the futures position to the cash position is known as the hedge ratio (HR). Ederington's second measure will be referred to as the partial hedging effectiveness (PHE); it can also be interpreted as the goodness of fit in a regression of changes in the futures price on changes in the cash price.25 As the hedging effectiveness does for full hedging, the partial hedging effectiveness represents the reduction in risk attributable to partial hedging. The three italicized concepts are not independent of each other; the interested reader can verify that any one can be derived from the other two. Thus we have

As an example, let us consider the crude oil futures market in New York. The standard grade is West Texas Intermediate (WTI), an important domestic crude. The delivery point is Cushing, Oklahoma; although not known as a great center

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of commerce, it is where a number of pipelines connect, so that crude can be sent from there to many other points in the United States. From daily price data over a period of about 3 years ending in 1995, the FHE for WTI with respect to the expiring future is calculated to be 0.9010, a high figure that explains the wide use of New York futures by commercial traders. The hedge ratio using that future is 0.9175 and the PHE, at 0.9013, is close to the FHE. Not all traders are interested in the expiring future, which is suitable only for hedging short-term commitments. Ederington's measures can also be calculated for more distant futures contracts. For the future that is second in order of maturity, the FHE is 0.8642, the HR is 0.8180, and the FHE is 0.8670. Going out as far as the tenth future in order of maturity, the three numbers are 0.6601, 0.5318, and 0.7009, respectively. Judging by the open interest, these FHE and PHE are still high enough to attract many hedgers. Hedging is also possible for varieties of crude oil that are not deliverable on the New York futures contract. An example is Alaska North Slope (ANS) crude, most of which is refined in California. Price data are available for ANS delivered in Long Beach, and they imply (using the expiring New York future) an FHE of 0.7929 and a PHE of 0.7935, not much less than for WTI. Thus hedging ANS in New York futures would seem to be quite feasible, but we do not know how much of it actually occurs. The ability of a futures contract to provide hedging for varieties other than the standard grade is important because it increases liquidity, thereby making the futures market more interesting for large traders. Thus the Brent futures market in London is used not only for hedging different North Sea crudes but also for Middle Eastern and African crudes. According to the Commitments of Traders data discussed at the end of Chapter 9, on the other hand, futures markets with low volume—the lumber market in Chicago is a case in point—are used by very few hedgers. 10.3.3 Market Equilibrium

The preceding argument applied to a single trader, who could turn out to be either a short hedger or a long hedger. Clearly, the total supply and demand for futures from each of the two types of hedgers can be found by aggregating over all such traders. It is also important to note that in any futures market the net futures position of all hedgers combined is exactly offset by the net position of all speculators combined.26 Now if the demand from commodity suppliers for short hedging just equalled the demand for long hedging from manufacturers and other users27 at any future date, the futures market would simply represent an exchange of agreements between these parties at roughly the expected value of the future spot price. The net position of all hedgers combined would then be 0, as would be the net position of all speculators combined. In the process, the risk faced by

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suppliers and users would be eliminated, which is one of the important potential benefits of futures trading. It has often been argued, however, that in many markets there is an inherent imbalance, due to greater underlying demand for short hedging among producers of commodities than demand for long hedging by manufacturers.28 This imbalance might reflect the fact the producers of raw materials have very little flexibility in their cost structures—hence face high risk to profits if prices fluctuate— whereas manufacturers typically have more flexibility through their ability to pass some of the fluctuations in raw material prices on to their customers, and therefore face less risk from adverse price movements. Such an imbalance would tend to make the futures price artificially low (relative to the expected future price) as producers of raw materials accepted less than the expected value of their commodities in an attempt to rid themselves of their high risk. On the other hand, those manufacturers who can fully pass fluctuations in raw material prices on to final customers without impairing demand for the product would only be willing to buy a futures contract at less than their expected future spot price. Such an underlying imbalance opens up an opportunity for the entry of speculators who have neither a long nor a short position in the physical commodity to soak up the excess of demand for short hedging. The speculator's goal here would be to go long in the futures contract at a price less than the expected future spot price. If expectations were confirmed, she would reap a profit on maturity by taking delivery at the low price specified in the futures contract and reselling at the higher spot price prevailing in the future. Of course speculators may be observed on both sides of the futures market—that is, some speculators will take long positions while others take short depending on how their individual expectations differ from those of the market. If the kind of underlying imbalance just described does exist, however, the net position of all speculators combined must be long in futures. Our reasoning up to this point may be summarized by saying that if hedgers tend to be net short in futures, then speculators must have an incentive to be net long, and this incentive consists in the futures price being less than the expected spot price in the future. Moreover, the reason the futures price can be below the expected spot price is that the hedgers will at some point prior to expiration have to cover their short positions by buying futures. When the hedgers do so, the speculators, being net long, will on the average gain. This observation leads naturally to a discussion of expectations.

10.4 THE ROLE OF EXPECTATIONS

One implication of the preceding argument is that the spot price and all the futures prices are more or less closely correlated with each other. It is not possi-

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ble to maintain, therefore, that the spot price serves to equilibrate the spot market while the futures market expresses expectations concerning spot prices in the future. If expectations matter at all, they must affect both spot and futures prices. As Hawtrey (1939) expressed it succinctly, "The futures price equally divides the bulls and bears at the point where supply and demand balance." By the same token, anything that influences the spot price must also have an effect on the futures prices. This idea is elaborated in two stages: Section 10.4.1 sets out an important theory of futures pricing, and Section 10.4.2 resolves an apparent paradox concerning the role of carrying cost in the determination of spot and futures prices. 10.4.1 Futures Prices as Predictors of Spot Prices

In his Treatise on Money (1930), John Maynard Keynes took the argument regarding speculators one stage further. If speculators are to accept the risk imbalance discussed earlier, they must be rewarded for doing so.29 That reward would comes if their long futures contracts became more valuable as they approached maturity reflecting a profit to be made by taking delivery on the contract and selling on the spot market. This profit reward will materialize if, on average, the price of a futures contract approaches the spot price on maturity from below. In other words, the basis is negative early in a contract's life {that is, s(0)

The Economics of Financial Markets

The Economics of Financial Markets

The Economics of Financial Markets